I continue to have this problem with all of my 5811 window sensors, even after replacing GC2 panel with GC3 due to unrelated failure (LCD stopped working in GC2).
I spent some time today trying to understand the issue. Your question “Can you confirm if they will send open and close signals to the panel?” is what led me down this path.
I’d replace the battery and no, it wouldn’t send open/close. So I noticed if bend the POSITIVE battery contact on the sensor just a HAIR - like a fraction of a millimeter, the sensor works after battery replacement and open/close/tamper is sent to panel property. I bought Panasonic CR2032s just like sensors originally came with, maybe the new ones are a fraction smaller diameter? Another possibility is the positive battery contact being bent back a little when I pop out the old battery with a screwdriver.
Just wanted to report back in case its helpful for anyone else. Didn’t need to mess with tamper contact, or negative contact - just the positive one. I’d had this issue on multiple 5811s.