The big problem Rhodesia faces is that non-recognition prevents it from carrying on normal economic relations, and it put tremendous strain on their resources for a long term war. Sanctions hurt.
I believe Rhodesia really went into difficulty when South Africa stopped supporting them after losing in Angola. Maybe if the South African intervention in Angola succeeded in defeating the MPLA/Cubans, then they may still feel it worthwhile to keep supporting the Rhodesians.
The other thing is that Rhodesia lacks the white population to keep white rule indefinitely. 5% of the country can't rule the other 95% without consent. The strange thing is that Rhodesia did not have a South African style apartheid. Blacks were not excluded from voting on account of race. Instead, there were economic and other restrictions that kept must excluded. Some form of relaxation would need to take place, and combined with some sort of land or economic reforms, might convince a substantial amount of Rhodesian blacks to support the government rather than the insurgents. I don't think if Ian Smith and the others were far sighted or enlightened enough to do so, but it was an option.
If the Rhodesian government could convince enough of the international community that black majority rule was possible in the medium term through their reform policies, they could have achieved recognition of UDI and been open to economic relations and foreign finance that might have been enough to keep Rhodesia in power, albeit with an ever increasing # of blacks in government. Ultimately, we'd finally see a black majority government take power within the Rhodesian system, perhaps by the 1990s.