That is exactly what the one sensor I had that didn't work, did.
I have returned it to Abbot (they have already supplied a replacement), but it comes over as the sensor responding OK to the initial connection, but then hanging when it starts trying to actually send data. I suspect there may be a small number of the main processor chips going around, that perhaps hang when reading the connection from the filament. May even be as simple as a fault damaging the filament when it inserts. What was interesting, was that when I removed this one, the filament fell off, but that has never happened with any other unit.
Bluetooth failures do happen, but the system recovers from these OK. When I tried the Libre2+, it was more frequent than with the Libre3, and on a couple of occasions it did not seem to self recover, till I actually scanned the sensor again. The Libre3 recovers every time. They happen for me, since I do things like arc welding, and nothing based on RF comms, works when you are doing this!. However in my normal day, I work in a lab, where the only problem is the Bluetooth can interfere with some of the sensors we use. When systems are working at PPB levels, introducing a source of RF is a problem.
My biggest problem at the moment, is the Libre3+ is not available in the UK. I have an allergic reaction to the Libre2 and 2+ (it is to the areas of plastic between the filament and the edge of the adhesive, or to the filament itself - though I would have thought this was the same material on the 2+ and the 3). Blister filling this gap. Takes weeks to heal, though I heal well normally. The 3 only has a tiny space here and I don't think my skin actually touches anything but the adhesive on these.