Cakewalk Pro Audio 9.x supports 96 kHz. The following suggestions apply to this version or higher; not sure about earlier ones:
First suggestion -- you changed the sampling rate in the Delta Control Panel -- did you let Cakewalk know about it? You should change the audio device properties to reflect that, or re-profile the card using the Wave Profiler.
Second suggestion -- what's your computer's specs? 96 kHz is tough on a machine (more than twice as much data streaming per second compared to 44.1kHz) and if your machine is an older one or its configuration is not highly optimized, what ran fine at lower sampling rates might just not at higher ones.
If that's the case, I would suggest you record at 48 or 44.1 kHz. Unless you have superlative gear in your signal path, you'll never perceive the difference anyway.