kentlowt,
I have Spybot 1.6.0.30 on 3 XP computers, one XP-Home SP2, one XP-Home SP3, one XP-Pro SP3. When it is idle, whether I click on the red cross at the top right of the main Spybot screen, or use File/exit to shut down the program the result is an instant return to the desk top. For comparison purposes all three have Avast Home Edition 4.8.1229 antivirus and Zone Alarm 7.0.483.000 Free Firewall.
I also look after a number of other home networks where individual computers have 1.6.0.30 or 31 and I have not seen the problem you describe before.
In case you have not already tried this, please clean out your browser cache and cookie stores, also clean up your temporary files. I would use Windows XP Disk Cleanup - Start->All Programs->Accessories->System Tools->Disk Cleanup.
If that doesn't overcome the problem, then my next suggestion is to completely uninstall Spybot (particularly if your update to this version was installed over the top of a previous version) and then reinstall from a fresh download from one of the sites at
http://www.spybot.info/en/mirrors/index.html
If you do this, I would also recommending using "This very small fix" from
http://www.spybot.info/en/howto/uninstall.html before installing the new version. During the installation you are offered some options, I would recommend NOT getting the updates during the installation, and NOT activating either Teatimer or SD Helper during the installation. These can all be done later. Once the new program has been installed, reboot, then start Spybot and exit again without doing anything else. See if the problem is still there. If not start it again and get the updates via the "Search for Updates" button in Spybot. Immunise, then exit again and see whether the problem occurs. If it doesn't start Spybot again, do a scan, fix any items in red (those in green are just user tracks so fixing (deleting) them is optional). Again once that's done, exit and see whether the problem occurs.
If it doesn't, start Spybot again, put it into Advanced mode, then goto Tools, then Resident and tick the SD Helper box. Exit the program - if the problem still isn't present, start Internet Explorer, check that the SDHelper add on is present, exit the browser. Start Spybot and exit. If it is still OK and you want to use Teatimer, start Spybot, goto Tools->Resident and tick the Teatimer box.
I know this has been rather long winded, but if you take it step by step even if the reinstallation doesn't overcome the problem, it may give an indication as to what is causing it.
The other alternative is using a utility like Process Monitor to identify what is happening during the delay period, but the success of that would depend on your level of expertise.
Please post back and let us know your progress.