Since the update to v2.27 mine has continuously been 'not responding' too. It doesn't seem connected to any event but this morning it was making my screen whiten periodically (frozen) and it happened every time I selected anything. Closed and re-opened it but was still the same. It was fine until this update and is used very regularly so I'd have seen it before if it was happening frequently.
Judging by the changelog, it may just be a coincidence that your troubles started around the time you upgraded to 2.27. Most of the changes had to do with categories feature this time.
I have it running on several machines and didn't find any new problems upon upgrade.
The only thing I can suggest is to check your hard-drives because I've seen this sort of thing happen before failure (read delays will hang a program for seconds here and there.) Tix does it's disk i/o synchronously and flushes writes to disk, so if the disk is having difficulties it will cause a pause in execution.
You could also check the File Diagnostic Log in the help menu > diagnostic tools to see if any filesystem calls are being delayed for long amounts of time.