Need Your Input Please - Techie Problem (Cell Phone)

Imagine this scenario:

Your 3G mobile phone data service works everywhere all the time basically.

Then you travel to a distant city and stay at a motel. When you have stayed there before, the connection was sketchy - sometimes good, sometimes bad, sometimes fast, sometimes slow. This time it is fast and clear from the time you check in at let's say 9:00 PM to 7:00 AM or so. Then it stops.

When it stops, the up arrow on the internet/data connection indicator on your phone lights up but the down one does not.

You go out into the city (where the connection has always been good - it's always just been this one hotel in this area that was a problem) and there is no way to connect at all. Up arrow but no down arrow. The phone part works fine.

You recently bought a new cell phone and change the sim card for testing purposes and the same thing happens. When the old phone works the new one does and when not it doesn't.

You've rebooted, restored the phone, plugged it in, wiggled the sim card and all those kinds of tech support requests multiple times.

The second night at the hotel about 10:00 or so you get a good connection until about 6:00 AM then it all goes away again including the ability to connect out in the big city during the day.

The third night the same thing happens.

What could be the cause of this?

1. It doesn't seem like it would be the phone since both the old and new exhibit the same behavior at the same time.

2. It may be something with the account where Internet access was disabled or something but why at the same time every night it goes back on and then off again in the morning?

3. It may be some kind of interference or placement of the hotel that interferes with the signal. But why would the signal be clean and clear at 11:00 at night and then completely go away in the morning. Also this wouldn't account for no signal out in the city during the day.

4. It could be an error at the phone company but it would seem that every 3G customer would be having the same symptoms.

Please, if anyone has any ideas please share them. We are going crazy. Tech support is going in circles and the only thing they can come up with when they go through each scenario is it's a 3G vs. 4G problem and we should upgrade this phone's plan. We know that 4G at this motel and in this city with this company works great on a new phone. But why would 3G have this kind of totally erratic behavior? And why could I connect on the same 3G plan last month out in the city but not now - at all.

Thanks in advance.
Mark