When I get it back from the repairman, it sounds great, feels great, but maybe a month after that, it feels like there are some leaks in there, extra airiness around the horn. Is this normal?
Actually, I've found this to be fairly common. I take my horn in about once a year, at most, and I play it a lot. What often happens is a pad or two gets replaced and some adjustments are made. The horn always plays much better, but within a couple of weeks to a month, it sometimes develops a leak (not always, but it's not unusual). I take it back to the tech, he fixes it in about 2 minutes at no charge, and then the horn is good to go for at least another year. What seems to happen is the new pads need to settle in or something. I'm not a tech, but I have a very good one who can do the job.
I'd suggest that whenever you get any major work done, especially new pads or an overhaul, pay attention to how the horn plays for the next month or so, then if there's any indication of leaks, take it back in and get a 'final adjustment.' That will usually do the trick. If you are using a new tech you might ask them about this. Any good tech will readjust the horn for free, if they did the work on the horn.
You shouldn't have to keep taking it back in multiple times, though. I've never had to return more than once in the short term after getting new pads, or whatever.