I couldn't find an answer to this question with the search option, so I asked theymos directly, and I'm posting the answer here because I believe that this question is also of interest to some other members of the forum.
Theymos replied that there is no strict limit on the number of messages we can have in the inbox, but warned that the PM page will become very slow if we have more than 30 pages of PMs and suggested that it is best to prune them periodically.
That hasn’t come into my mind because there are a lot of threads that are more than 200 pages. So even if your PM list becomes more than 200 pages, it shouldn’t be an issue. You may visit the wall overser thread that has more than 3600 pages. That’s why I wasn’t concerned about the PM pages.
However, as theymos said, it’s normal behaviour if the page becomes more loaded; the loading time would increase. Unless you delete your PM, then it will keep increasing. For me, I try to delete PMs that aren't important. So it will reduce time to find necessary PM and loading time as well.
