I had the same loop restarting problem with my Atrix 4G right after I updated to Gingerbread. I called AT&T tech support since the phone was still on the one year warranty. The very nice technician I spoke to walked me through every single step of the hard reset process and waited patiently with me for a really long time for the sluggish phone to respond. After numerous tries and numerous failures I finally got the factory reset done, it took me at least five hours to do that. After the wipe the phone had a clean Gingerbread system and functioned without a problem. I was relieved and started installing some apps again, some of them require running in the background occasionally, nothing too intense. But the phone became sluggish again after a certain amount of apps was installed, and this morning it started to do the loop restart thing again. This time I suspected it was a simple RAM problem. The phone actually CAN'T handle that many apps running simultaneously and when that happens it slows down and eventually starts restarting. So I hit the power button as soon as it restarted again and chose "turn off phone" before it got a chance to load the RAM with all those apps. It turned off and stayed off, turned back on once, I did the same thing. I left it charging and went to cook lunch, when I came back to check on it, it turned itself back on again. But this time, it started up and loaded everything without a problem. Probably took it a long time to do that but it made it eventually. I went into my app manager and started deleting apps and kept only the essential ones. I deleted most of the games since a lot of them have junk processes running in the background every now and then without you knowing. The phone seems to be in good shape now.
Here's a few things I've learned so far:
1. When the phone starts to slow down, it's an indicator that it can't handle the tasks right. Delete unecessary apps or RAM demanding apps and games would usually help, don't wait until it starts loop restarting. You'll know that the phone is in good shape once it starts running faster.
2. Summer is coming and Atrix DOES tend to heat up. High temperature affects CPU performance and it doesn't matter if it's a phone or a computer. I took off my Otterbox Defender case because it's too warm a jacket for the phone in the summer. And I kept the phone in a cool place when it's charging. Both seemed to help.
Most importantly, I've learned that Google is really not as responsible as we assume it is when it comes to Adroid development. I hate to say it. But it's true. The numerous problems that occured only after the system update proved that the hardware is not the one to blame but the software. They really screwed up. You DON'T screw up a phone operating system like that because it could actually put people's lives in danger. We've all come to rely on our cells and bringing an unstable phone with me means when it overheats I can't even call AAA if my car breaks down. Blackberry never left me hanging like that, nor did iPhone or Windows Phone. Just Android.