With green compound on leather, in particular, I've found it'll last quite a long time. I've been in the habit of wiping down or cleaning my strops when they start looking more black than green. Having said that, I might not need to do it quite so often. I've also noticed, with my newly home-made strops, the performance really seems to improve after the compound has been applied, cleaned, and re-applied a couple or three times. It seems to make some sense to me, that it takes a re-application or two for the compound to get thoroughly distributed and firmly embedded into the leather. After about the 3rd cleaning/re-application, my strops are a LOT more effective than when new. Not just with green, but with other compounds I've used (diamond paste and Simichrome polish are others I like).
I'd highly recommend not 'caking' the compound on. It works much better when the leather is just 'dusted' with the compound, so it still looks like leather, but with a greenish tint to it.
If you like how your strop is performing at the moment, I'm betting it's fine. If you do notice performance dropping off, and the leather is starting to look pretty dirty, then don't be shy about cleaning it and re-applying compound. Great thing is, the compound is cheap, and the leather will stand up to many, many cleanings over time. So there's really no harm in cleaning & refreshing it, even if it might not be absolutely necessary. You'll get a much better feel for what it needs, after using it for a while and seeing how it changes with a few 'sprucing up' sessions. In the short term, you might just wipe down the strop with a dry paper towel, when it starts showing more of the black stuff on it. That'll keep it working quite a while, in itself.