I know that sick feeling
Him leaving that first time was more complicated then it would be now because we were still married, he did rehab, this was our family home, we were going to do some counseling etc. Honestly it is a bit of a haze but I believe it was 4-6 weeks from the time I said we were 100% getting divorced and getting into the apartment he lined up (low income - guess you can just drink yourself silly instead of work and get the government to pay your rent here).
I regret most of it and wish I'd have followed through on the initial court order. Nothing changed while we were under the same roof except it caused extreme turmoil for the kids and I. He was mad and panicky about it and took it out on me. It did not help him get on his feet. Not one bit. It just gave him a free no responsibilities attached place to be for a few more weeks.
If it was today, and he was in my house and I needed him out and he *really* had no where to go, I'd hand him $100 (which is at least two nights in a motel around here) and tell him to leave that very day.
He isn't using the time staying with you to figure anything out or get on his feet. He's just waiting for you to throw him out so why keep him waiting?