We have several customers using R4s and Zigbee Pros with issues. Basically you reboot the Zigbee and remote and they work again for a while. As best as we can tell, it seems to be something related to the remotes that go to sleep most of the time (but not always). We are running the latest firmware on both the remote and the Zigbee (I see the most recent Zigbee firmware is 2009 and attempted to address some of these issues).

The symptom as described to me is typically the user will be at the remote and it will freeze on the profile selection screen and the remote is non responsive until a reboot.

AMX tech support hasn't been much help, I'm just wondering if anybody else had run into this and figured out a solution. As you might imagine, customers aren't particularly happy when they spend zillions of $$ and have to deal with rebooting their stuff.

Are you an AMX dealer? R4 firmware was updated Jan of this year. Zigbee remote/gateway FW each have two parts, module and radio, both need to be brought up-to-date. I have encountered several installation where only one part was updated.
Check logs and buffers for overloaded queues. 250 or less messages to the gateway at a time.
Verify channels on Zigbee to ensure no over-lapping wifi channels. Zigbee operates in the same freq range as wifi and there are only 4 channels that do not interfere.

Been having this issue for 4 years on one job. Replaced everything and it still keeps happening. Works for six months or so then the remote stops communicating. We have to reload firmware to everything and then it starts working again. PITA!!!

Maybe we have not faced this exact problem but we are keep having constant problems with R4s to the point that I hear its name and I want to run...

We have a dozen or so in the field and other than one that likes to do the random 'no-sleep' issue, they all work great. Lots of R3s as well.
Biggest thing we have found is zigbee channel assignment and managing data flow to the remotes. Keep the gateways on 15, 25, or 26 and then minimize traffic (esp levels) to the remotes and they work great.

Thanks for the advice. We are AMX dealers, my guy is on site now. AMX got back to us and suggested a few things. We are already running the most recent publicly available firmware on both the R4s and Zigbees, but they said they have a newer version that may address the issue that they haven't made available yet. We're going to give that a try. They also recommended disabling Bonjour on the Zigbees. Fingers crossed. This customer was so frustrated he actually broke the screen on one of his R4s by pounding on it with his finger trying to get it to work.

It seems that this might be a good time for you to try to sniff what is going on over the air.
I'm using the Perytons Analyzer (www.perytons.com) and I'm quite happy with it.
They support a quite nice of protocols including all ZigBee profiles as well as RF4CE and 6LoWPAN and what is (more) important, they provide a free 30 days eveluation download so you can try them out and even capture your live data (even in the 3 x RF4CE channels during voting simultaneously) if you have any of their supported front-ends.
You may want to try them out.
Good Luck!