I have one of these, don't know if it's the same model. Mine is a TD8840T
Occasionally it will get into a state where it disconnects and keeps trying to reconnect but fails, logging into the setup page and rebooting makes it connect.
I tend to blame this on the BT line, a while ago it started doing it very often, this coincided with the intermittent appearance of noise on the landline. I reported it to BT who sent an engineer who traced it to a bad pair from the pole head. He swapped it to another pair and not only did the noise go away the router stayed connected for weeks. It has done it again occasionally since, though.
I think what is happening is that the router and the exchange equipment negotiate the highest speed possible, if the line gets noisier this speed becomes too fast for stability, rebooting or in your case factory reset makes it renegotiate a slightly slower speed or possibly a different protocol whereas the automatic reconnect just tries to reconnect at the previous speed.
The "modulation type" seems to vary between "Auto detected" and "ADSL_G.dmt".