Anyone Else Having Linear E3 Panel & Reader Problems?

Readers have been replaced/swapped and doors still behave the same way.

Full notes:

• I started in the security field in 1985. I have installed dozens of access control systems in that time, most of them Linear systems or their IEI predecessors. I have never had this issue come up before.
• I installed a Linear E3 Elite panel for a good customer in June 2016. We installed 3 access controlled doors to the system, 2 with Linear P300 readers and 1 with a take out/used Honeywell OmniProx reader. All were programmed and tested fine- cards read good, reader LEDs change from red to green properly, all works well as far as we can see.
• After a few weeks the customer told us that they had to present their prox fobs twice to be granted access sometimes. I investigated, verified the complaint and discovered that if the reader stays idle (no reads) for about 6.5 minutes, the first presentation of the fob beeps the reader but its LED stays red and access is not granted. If you present your fob again within about a 6 minute window the reader LED turns green and access is granted. The effect is like the reader falls asleep after about 6.5 minutes. 
• After about 6 months the customer wants to change the readers to Keypad/Reader combo units on 2 office doors. We install the P640 combination keypad/prox readers on those doors. A week or so goes by and the customer tells us that the same effect of the readers falling asleep is noticed. I changed those 2 P640 to new P640s. Nothing changed. I changed the reader/keypads again to a different manufacture,  HID, I believe. Nothing changed. I replaced those readers with some from AWID. Nothing changed.
• During this whole time, the Honeywell reader on the back door has logged no complaints at all. I test it every time I go to the site and never find a problem with it, the back door unlocks on the first prox read after periods of extended inactivity. The 2 front doors continue to act like they fall asleep.
• We add a 4th reader for enrollment of cards at the receptionist desk. This reader logs no complaints at all, ever.
• We call Linear tech support many times in an attempt to solve the problem. They want us the wire readers right to the panel, ask about wire type and length (Wire is composite access control cable with a shielded, twisted pair cable used for reader power. LED control and data, length of wire run is about 75 feet direct from the controller to each controlled door. There are no splices in the cable, only at termination using irreversible crimp connectors filled with dielectric grease). We connected readers directly to the panel in an attempt to troubleshoot but since at the time this was done we hadn't determined how long it was before they fell asleep, troubleshooting is difficult because you have to read a card and wait an indeterminate amount of time and try a card read. If it works, this resets the sleep clock and the troubleshooting timing cycle begins all over again. It takes several hours to determine that the readers will unlock the door on the first try if a card is read every 6.5 minutes. If you wait 7 minutes, you have to try twice before the door unlocks.
• During this time, we install 2 Linear expansion clients in 2 separate buildings connected by network. The keypad/readers and readers in these locations work perfectly with no issues. We actually used the original P300 readers we took out of the office when they wanted keypads instead and reinstalled them in one of these sites- they have been flawless. The problem at the office continues, but only with the 2 front doors- doors 3 and 4 work perfectly.
• We get an RMA for a replacement controller board. We go to the site, backup the database, use the SD card from the old system in the new board, power up the new board and restore the database. The software version of the controller and the clients match, the new controller software version is the same as the old board. Everything works fine except the sleep issue with the same 2 readers persists. We power down the system, take out the old SD card and install the new one that came with the new board. Power back up and reconnect to it, restore the database again and all works well, except, you guessed it, the readers still go to sleep.

I'm out of ideas, any suggestions?