I have a 2001 chevy suburban 1500 and when I turn it on, it doesn't stay on, so I have to do it again and then it stays on.
When I turn it on in the morning I have to give it gas, otherwise it wont stay on. What is the problem I'm having?

 

Sounds like your fuel pump is losing pressure when shut off (very common in these suburbans, tahoes, silverados). Basically you are just priming the lines when you first crank it over. The lines are supposed to stay primed because it is a returnless system. When you give it gas you're essentially helping it do its job. Obviously your pump is still working somewhat, but it's most likely on it's way out. You can check the fuel pressure to confirm.

Hope this helps!

 

There is a check valve in the fuel pump assembly. This is what is bad. When my Silverado did that I put a check valve in the fuel line by the tank and the problem was solved. After about a year I sold the truck and the check valve was still doing the job with the same fuel pump.