I have clocked a lot of hours blurring stuff for reality TV. There are a few things that can happen that tend to ruin everything.
If you trim the clip with the blurs, it will move the keyframes, since I think they’re always elastic keyframes for the blur effect. This doesn’t sound like what you’re talking about though.
Are you using the tracker? That will create an offset. I usually set the beginning and end keyframe to the same thing, turn on and run the tracker, then fix the other keyframes as needed. You can try toggling the tracker on and off and see if that has anything to do with it.
The most annoying thing for me is when I accidentally add a point to my blur shape when I’m halfway through animating the blur. Avid will try to add it to the other keyframes and often ruins the whole thing. If you don’t catch and undo this immediately, you might have to start over.
I’ve also run into some weird things where the shape doesn’t actually move where I drag it. The only thing I’ve been able to do there is restart Avid, but there may be another solution.
Also, I don’t know how you work, but I find that you save yourself a lot of trouble if you just apply the blur effects to empty filler instead of the clip itself and use a separate one for each shape. Sometimes I use the paint effect instead, set to blur mode. With the paint effect, you can use one shape set to blur and another shape set to erase. This can be easier for some complex shapes, and it also works for a vignette effect.
Hope I at least told you something useful.