SQL & PL/SQL :: Function Very Slow After Oracle Upgrade

We have a function that is called in various other PL/SQL packages, and performance has always been very good. On 29th Sept we upgraded our db to 10.2.0.5.0 and since then, a package that calls the function has gone from ~4mins, to ~2.5hrs to run.

In PL/SQL Developer, a simple select that calls the function has gone from ~0.5secs to retrieve the first 100 rows, to ~12secs. I ran a profile of the main package, which highlighted the where the bottleneck was (a fetch from an explicit cursor). Running an explain plan on the cursor SQL doesn't really show up anything untoward.

However, I found that if I subtly changed the cursor SQL, (so that it did the same thing, but was written differently), it fixed the performance problems.

where ade_start_date between cpDate-cpDays and cpDate-1
/*and ade_start_date < cpDate
and ade_start_date >= (cpDate-cpDays)*/

From this, we thought that there may have been a bad cached execution plan which the change of code forced a recalculation of. However, about 2 hours later, the changed code ran slowly again. So a further subtle change was made, which fixed the issue again. Until this morning, when it was running slowly again.

This feels like it is CBO/stats related potentially, but is out of my area of knowledge unfortunately. We have our DBA investigating this, but there may be things I can test to narrow down the possibilities in the meantime.