There isn't any limitation published for minimum time before shut down because the APU has an electronic control box that ensures thermal stabilization of the APU before shutting down, so even if you push the master push button to off, it will continue running till the APU cools down then shuts down, however there is a minimum time for consequent starts....3 start attempts and then wait 60 minutes before attempting another 3 starts and so on....
They probably do that to make sure that they have a pneumatic source readily available while engine shutdown, in order to deal with any engine tailpipe fire that might happen during shutdown(though its not a very common thing to happen)......It is sure though that by shutting the APU so fast after starting is a waste of APU starter....and it would be better to have a GPU and an ASU ready at the stand while shutting down the engines, unless of course they don't own the ground equipment and they have to pay for using it, in that case a starter replacement every once in a while doesn't sound so bad.