Sounds like the TeenAgent engine opens too many files at once.
A quick look at its resource.cpp confirms that it has 9 file handles open for the main .res files at all times, and then there's the theme file, save files which need handles of their own, and whatever else.
To be on the safe side on PSP the number generally shouldn't exceed 10 or so. Maybe the number of open files in resource.cpp can be reduced.
Please file a bug report for this issue!
Teen Agent: cannot save
Moderator: ScummVM Team