His first invasion of England failed partially due to extremely heavy rains. WI: His ship sinks while returning to Brittany and he drowns. Does that leave anyone strong enough to rebel against Richard III? Does this mean that Richard will keep the throne?
There is virtually no-one - even Henry's claim was remote and he certainly wasn't considered any great threat until Richard III's deposition of Edward V unsettled the Yorkist apple cart.
After Richard III - there is only one direct male line descendant of Edward III left - Edward Earl of Warwick (Richard's nephew)
In the Lancastrian descent the claimants are the now childless Lady Margaret Beaufort the nearest Beaufort claimant after her is going to be her cousin Eleanor Beaufort Countess of Ormonde (daughter of the 2nd Duke of Somerset) she has two daughters.
After Eleanor her sister's son the Duke of Buckingham would be next but he is dead and his children have a Woodville mother and are still very young in 1485.
Possibly, but more likely Richard's enemies just find another pretender. a real one if any can be found; if not then a Perkin Warbeck type of impostor. Just so long as he's unmarried and so free to wed Elizabeth of York, anyone will serve.
Richard had already arranged to marry Elizabeth of York to the Duke of Beja. Her younger sister Cecily had already been married to Ralph Scrope, a loyal supporter of Richard. Anne was engaged to one of the Howards. Catherine was only six and Bridget only five, but as they got older Richard would have tried to marry them off to foreigners or loyal supporters as well.