I have a small datasnap server written in Delphi 2007 that accesses the BDE. It works fine on Windows 2000 and XP but from time to time (actually quite regularly) on Vista
the resolution for the error is by increasing the shared memory available for the BDE.
You haven't mentioned if you've tried adjusting the virtual memory settings. BDE error 2501 is an "insufficient virtual memory" error. Some articles that may help:
Andy's answer link to www.torry.net is for some $30 software package that "claims" to fix BDE errors. I'd comment on it, but I don't have the reputation points. (...but someone else could...) The link doesn't work, but if you search for "BDE Setting" you'll probably find it. I can find no evidence or reviews that it works. Download unsigned exe's at your own risk... (I'll pass)
I've found full solution for each Pc on x64 systems.
BDE-Setting x64 v.3.15
http://www.torry.net/news.php?id=262