the above did not help in my case. i have a Nook tablet 7. my wife has the same device and the kindle app works fine, but on mine, it is either disappearing or keeps reporting a problem. have tried the above several times and a couple other answers i found thru google. it dawned on me that it could be the extra gb card i added to the nook. sure enough, i removed it, reinstalled kindle and it went into the built-in memory on the tablet, and works like a charm. reinserted the exrta memory and everything working fine. so it seems that app didn't like being put into the extra memory slot. seems strange as the other apps i have downloaded work fine with it.
just my 2 cents worth,