I use Freeserve broadband & I can stay connected as long as I like.
I have the internet settings set so that the line is dropped after 20 mins of inactivity, but that's just a safety precaution against hackers whilst I'm away from my PC.
I have only had problems connecting twice, once when the equipment at the exchange failed & I was without connection for a fortnight (got compensation from Freeserve for days I couldn't connect, even though it wasn't their fault, BT whose fault it was, refused my compensation claim, typical), and once during a bad thunder storm. Other than that, no probs.
Do you live far from the exchange, because if your line is at the far limit then any line noise will throw you connection. Get Zen to look at their end, and BT to check the line.