No fob detected, intermittent starting. Shuts down while diving.

What is your question?

Bought it used a month ago with 155,000 miles. 2005 Cadillac sts v8. Car runs and drives great when it will start. Been getting a 'No fob detected'. The problem is intermittent. Sometimes the car starts no problem for 3 days, sometimes it doesn't (No fob detected), sometimes it completely shuts down while driving (No fob detected). Tried reprogramming using the 10 minutes 3×s method and didn't work. Tried putting the fob in the limp mode slot, didn't work, tried changing the fob battery, didn't work, tried walking away with the fob and returning using the key to open the door, didn't work. While the 'no fob detected' issue is happening, it will sometimes start but stall, sometimes it will start and run but not allow me to put it in drive, sometimes it won't even let me shut it off unless i open my door then it shuts off by itself right away. I've tried every trick in the book that I've seen on the net. I'm thinking either a new fob or a receiver issue. No rhyme or reason to it

What makes this problem better or worse?

Nothing, happens in all scenarios

How long has your 2005 Cadillac STS had this problem?

A month