What series of events can ensure that Spain can remain relatively strong after the War of the Spanish Succession?
Not many.
Even if it doesn't weaken, other powers are ahead of it and getting more so.
Does it have the resources for even major reform to access so far as the government is concerned?
Spain doesn't have to be a Great Power - even though at this point in OTL, Prussia was on its way to Great Power status despite its size and lack of colonial possessions.
What I mean is a better outcome for Bourbon Spain - one that continues the relative momentum set by the early Spanish Bourbons instead of derailing as in the OTL 19th century.
Prussia has valuable assets like a middle class and a functioning bureaucracy though. Spain seems short on those (Which are necessary for its long term future, with or without great power status)
A worthy point. Perhaps if Charles III's administration isn't virtually erased by his lackluster son Charles IV, then Spain could do better.
Alternatively, the Napoleonic Wars destabilized Spain, so getting those out of the way can help.
The uninspiring Charles IV was bound to ascend the throne in the late 18th century, and his son proved little more competent anyway. That said, having an abler valido (proto-prime minister) than Godoy, a guards officer and the Queen's lover would have helped.
Avert Napoleon's invasion, along with anything comparably traumatic.
The uninspiring Charles IV was bound to ascend the throne in the late 18th century
Actually, in the 19th century, the best bet for Spain would be more conflict not less. If she'd let go of Cuba, and fought another Carlist war to put them in their place, Spain could have maintained at least some status and power in the international stage. Compare to Italy or Austria-Hungary prior to WWI.
A Spain with no colonies and four civil wars in a row is in better situation than how Spain was in 1700?
The 'Carlists are overrated' should be included in the misconceptions thread BTW. The Carlists were crushed and done for good in the 1870s. If they had any power or political traction left they would have tried something in 1885 when there was a king-in-utero or in the aftermath of the '98 disaster. True, they made a comeback in the 1920s and 1930s but that was in line with the general trend of militaristic groups arising in interwar Europe. The 1930s Carlists were as different from the 1870s ones (or the 1870s from the 1830s for that matter) as the first and second incarnations of the KKK were.