OK, well at this point I probably will have to send you a custom firmware that prints debugging information on the LCD screen, to help understand the issue. I am mostly puzzled that you said Stefan’s firmware worked for you at least for several days. This firmware (2.1.9(5)) is very similar to Stefan’s firmware, except it turns on broadcast when processing DHCP. But if you are already using static IP, then it will never turn on broadcast. So I am puzzled why this works much less effectively than Stefan’s firmware. In any case, I can generate a custom firmware with additional debugging information on the screen to help understand the issue.
It’s certainly also possible that your ENC28J60 module has a defect, in which case you can send a support ticket so we can send you a new one (or you can buy one from amazon: https://www.amazon.com/ENC28J60-Ethernet-Network-Module-Arduino/dp/B01FDD3YYW).
Some other options to consider are: 1) use a secondary router (or VLAN if your router supports VLAN), as described in a post above); 2) try the W5500 Ethernet module as described in this post: https://opensprinkler.com/forums/topic/instructions-for-testing-os-3-2-with-w5500-ethernet-module/)