Sounds like the 5800's are periodically failing their supervisory check-in. I have a Lyric system on the bench, but have not installed any of them yet. I do not like the all-in-one units because I think they have some drawbacks in terms of versatility.
One drawback is that you mount the main control on the wall, wire power to it, and then begin the GO NO-GO testing. Then you find out that a few of your transmitters are in a null spot, and this null spot is large, or there is interference. And no matter where you test them around the opening you'll get intermittent signal strength. With separate components you have more options, moving the receiver, adding a repeater, and hardwiring if necessary.
Sounds like your particular install has few options. Are the 5818MNL's installed horizontally or vertically? Sometimes it makes a difference.
When doing a GO NO-GO test, do you check it once or twice? I usually check it five to ten times, and I'm looking for just one miss. If it misses once, I recheck it multiple times for another miss and if that happens I look for another location.
On the 5818MNL, I use masking tape and put the sensor on one side of the door. Then do the GO NO-GO test. If it passes my test there, I tape it to the other side of the door and do the same. Then I tape it to the jamb and do another test. If it works fine in those locations, I install it. This takes more time, but a call back take a lot more time.
Are the signal problems happening at certain hours of the day? Could the customer be using a device that creates interference?
I had a particularly problematic install using a Lynx 7000, which I think has a lower powered receiver. This might be the case with the Lyric, it may have a lower powered receiver as opposed to the 5881's. This particular install had a bad null spot with two windows and the 5811's were not testing to my standards. The main control had been installed, was 30' away, and large sensors like the 5816 would not be acceptable to the customer. I found a smaller surface mount sensor made by Resolution Products, which was compatible with Honeywell. These sensors seemed to have a stronger transmitter, tested to my standards, and have been working fine for a few years. I don't think Resolution Products make a recessed transmitter, but you might check.
Also, the new Honeywell 5800mini seems to be pretty good. You might see if the customer would find these acceptable.