You are exactly correct.  As I look more closely, I find that the tempo is not exactly precise.  I then imagine that when I convert to a groove clip, the fact that the timing is a little off throws the whole conversion.

When you are recording clips that you intend to use as loops, use the metronome.
This ensures that you are in sync with the project clock.
Also Groove Clip almost always miscalculates the beats in the clip.
If you have a clip 12 measures at 4/4 it would be 48 beats.
Verify that beats in clip shows 48. Most likely it does not. it's probably something weird, like 37. Change it to the correct number, and you're good to go.

jvanbeek
You are exactly correct.  As I look more closely, I find that the tempo is not exactly precise.  I then imagine that when I convert to a groove clip, the fact that the timing is a little off throws the whole conversion.

 
I doubt that's the problem. The whole point of a groove clip is that you can take something at one tempo and it will work fine in other tempos.
 
Can you post a screen shot of the loop construction window when you double-click on the clip? You can upload images at imgur.com and post a link here that will place the picture in the post.
 
I'm sure it's something simple. Please note that slowing down a Groove Clip will give MUCH worse results. I'm not sure what the original tempo was of the loop or of the project, but if you slow down a groove clip by more than 10% or so, you really have to know how to edit the clip to have it sound decent. On the other hand you can usually speed up by 100% or more. If I'm going to be creating a groove clip, I usually record at 80-100 BPM.

I'm sorry for the huge delay in my response, but my job prevents me from working with my music.  I believe that the problem was due to the fact that my computer had a virus.  I was able to get rid of the virus and everything seems better.  Thank you all for your time and suggestions.