The problems Sega experienced in developing a suitable successor the the Genesis/Megadrive, problems which led to it's ultimate demise as a console manufacturer, can be traced back to the development of the Sega/MegaCD and the bitter rivalry that emerged between Sega of Japan and the Western branches of the company.
In Japan, the MegaDrive (and the Master System before it) had always been a struggling niche system, lagging behind both Nintendo and the NEC PC Engine (aka, the Turbo-Grafix). When the MegaCD was released in Japan in 1991, in response to the introduction of a CD based attachment to the PC Engine, the new Sega add-on attracted a fair amount of interest from Japanese third party developers, eager to develop games for the CD-ROM format, and as a result, the MegaCD actually boosted the sales of the MegaDrive a bit in Japan. As the MegaDrive had performed poorly in Japan anyways, the prevailing logic at SoJ was that the next console should be a CD based machine built around all-new hardware.
In the West, however, the situation was very different. The MegaDrive was already the dominant console in Europe and other PAL regions, owing in part due to the popularity of, and it's backward compatibility to, it's predecessor, the Master System. Furthermore, in North America, the Genesis had managed to attain a brief ascendancy over Nintendo in 1992 and 1993, so Sega already had the dominant hardware in the West. The MegaCD prototype sent by SoJ to SoA was allegedly deliberately sabotaged because SoJ was afraid of what the West could do with the new hardware. The SegaCD/MegaCD was not released in America until the end of '92 ('93 in Europe) and, thanks to the initial issues with the prototype, game development for the console in the West was delayed, and so the Sega/MegaCD was severely lacking in third party developer support outside of Japan, and subsequent sales of the Western version of the console were poor.
So when the time came to develop a successor to the MegaDrive/Genesis, SoJ found themselves at odds with their subordinate western branches. For SoJ, the answer was the Sega Saturn, a stand alone 32-bit CD based console with all-new hardware that had absolutely nothing to do with the Genesis. Sega's Western branches, however, after the poor performance of the Sega/MegaCD in those regions. preferred sticking with the tired-and-true Genesis/MegaDrive hardware, and were in favor of the 32X; a far cheaper cartridge-based 32-bit upgrade for the Genesis/MegaDrive. While many in hindsight have claimed that the 32X was doomed from the start, pre-orders of the add-on reportedly exceeded a million units in the US alone, so there was certainly sufficient interest in an upgraded Genesis/MegaDrive in the West.
However, the hardware of 32X, as an add-on, proved problematic for programers, who found it difficult to fully harness the power of the 32X via the Genesis/MegaDrive. Furthermore, the console did not come with a pack in game or new controllers, and initially retailed at $170 (it was rapidly dropped to $150). Additionally, an upgraded Genesis/MegaDrive with the 32X hardware (along with additional upgrades) built in and more thoroughly integrated into the system, and thus, easier to use, was in the planning. This “Sega Neptune” would have retailed for $200 and would have included new 6-button controllers and a pack in game, which in turn discouraged gamers from buying the 32X add-on unit upon release. Even more damning for the 32X, Western developers began receiving their development kits for the Saturn at the same time as the 32X kits, and SoJ was adamant that the Sega Saturn would be the wave of the future. As a result of all this, the 32X was dead within a little over a year of launch.
Unfortunately, the Saturn proved to be just as problematic as the 32X. SoJ's new baby was extremely expensive to produce, and as such, was very expensive at retail, launching in the US at a whopping $400. Furthermore, the Saturn was notoriously difficult to program for, meaning that games on the Saturn generally looked worse then their incarnations on the Sony Playstation, even though the Saturn had more raw horsepower. Many third party developers simply decided to forgo the Saturn (and the 32X) altogether, giving the Playstation a much larger library of games. After a disastrous early launch, the Saturn swiftly fell behind the Playstation, both in sales of hardware and software, and combined with subsequent price drops needed to compete with the Playstation, and later, the N64, drove Sega into massive debt.
Things were even worse for the Saturn in Europe and the PAL regions, until then Sega's strongest markets. Generally speaking, PAL gamers like to get the most out of their older consoles, meaning that aging systems generally have longer lives there then in Japan and North America, and new systems with backwards compatibility with the older consoles are looked upon much more favorably. The Saturn was an expensive, all new piece of hardware with few games for itself and could not play any games from older Sega consoles. Even worse, because Sega was already loosing money on the Saturn in America, Sega made the decision to stop production for the Genesis/MegaDrive and it's add-ons right around the time the Saturn launched in Europe, infuriating Sega fans there, many of whom bought Playstations instead. The UK, traditionally a loyal Sega stronghold, was the main exception, and Sega consoles continued to enjoy popularity there even into the Dreamcast era.
But by the time time the Dreamcast came out, it was much too late. Despite a massively successful launch in the States, Sega was already drowning in debt, and the Dreamcast was swiftly overshadowed by the PS2 thanks to Sega's poor reputation with consoles, lack of DVD capability (which was a result of lack of money at Sega), and a lack of copy protection for the console (which actually resulted from the rushed development of the Dreamcast, to get the console to market as fast a possible to attempt to recoup from the losses of the Saturn).
So if you want to keep Sega in the console business, you need to go back to the Sega CD era and get Sega of Japan on the same page as Sega of America and Sega of Europe. SoJ needs to actually help with launching the SegaCD in the West, rather then attempting to hinder their efforts out of petty jealousy. Then, you need SoJ to actually work with SoA/SoE on the development of the next console. SoJ was right about one thing: the next console needed to be a stand alone CD-based system. But the console also needed to be reasonably priced, easy to program for, and (especially for PAL regions) backwards compatible. If the Saturn had been built off the existing MegaDrive/Genesis hardware, that would have saved Sega a lot of money in development and production, would have made backwards compatibility a matter of design, and also would have made programing much easier given the hardware similarities of the new console with the MegaDrive/Genesis. I'm envisioning something like the Sega Neptune, but with a CD drive built in, while still retaining the cartridge slot. Such a console would likely have retailed for $300 at launch, making it competitive with the Playstation, and would have maintained the loyalty of gamers in America and Europe via backwards compatibility. With a successful 32-bit console under their belts, Sega could have taken more time to carefully develop the Dreamcast, avoiding the critical errors they made in desperation while creating that system. After that, well, who knows where Sega would be today.........