Doing a Search of the Corolla forum would've helped you equally as this has been discussed plenty of times. Time for a new starter dude, yours is suffering from heat soak, that is when it's hot enough in the engine bay (ex. after a long trip) the starter will not work right away, but if you wait a little while eventually it works again.
I had the same problem with my 89 GTS for the last year or more, now that I'm trying to get it ready for winter, the starter will not work anymore. Time for a rebuild.