I've been lending with Kiva for 2 1/2 years. My own default rate is 0.4% Kiva's default rate since its inception is 1.00% I think that is exceptional, especially when you consider that Kiva is all about lending to people all over the world who have little access to credit.
I see no reason at all to worry about Kiva's stability.
However, there is a risk in getting into Kiva lending just to cycle money through and maximize miles/points/cash back. Some folks who do this a lot (withdrawing all or virtually all of their money each month) now have to wait weeks for their withdrawals to be mailed to them. Kiva does this rarely, but it has happened.
As far as I know, making occasional withdrawals is not a problem.