Most of Mugabe's propaganda revolves around the idea of a massive conspiracy against him by Britain anyway.
Invade Zimbabwe and the population will rally around Uncle Bob (they have more than enough reason to rise against him - genocide, sky high rates of inflation, ethnic/political cleansing, etc... but are kept down by fear and "respect" so what the fuck makes you think war with the old colonial master will make that situation any different), more of our soldiers will die, and the possibility - actually, the near certainty - of civil war in Zimbabwe with the conflict infecting other countries.
borders in african countries - even in SA - are largely artificial creations anyway ... what makes you think that the resulting conflict won't infect anywhere else? the invasion of zimbabwe will mean the mass exodus of thousands of people from the country, even more so than what's happening already, which as we have seen in south africa already means the possibility of violence in that country, as well as others - the knock on effects of the Rwanda genocide are still being felt today, what makes you think that it won't destabilise the whole fucking region??