Oh, okay ...
Packet routing issue, a janky
edge router, or whatevs. If that's the case, changing DNS servers won't do jack. You won't be able to contact them anyway (arguably).
I had a similar, ongoing problem at my former ISP. The whole system would go down nightly, around 2 AM. Wiped AZ customers off the grid.
They only had one person working at the noc, at night, and if he wasn't paying attention to the monitors, we'd be down for hours.
To make the situation worse, there was no telephone tech support outside their regular business hours, only email.
They finally gave me the phone number for the noc (no bull) so I could call it directly. Looking back, it was funny as hell, but not so funny at the time, believe me.
Anyway, it took them months to find the flaky edge router. It never did go belly-up. It would just spaz out every night.
Turned out it was somewhere over in Cali, at one of their vendors. After they replaced it, I never had another problem.
EDIT
As fate would have it, I spent the last two hours shredding docs, and the rascals billing receipts were in the pile.
This is the mom n' pop I was using in the Valley:
http://www.cybertrails.com/ (noc was on Lone Cactus Dr)
Why did I go with them, you might ask ?!?! They were offering *free* dial-up as an enticement to signup, which was crucial to me, at the time.