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If it does, then the anti-theft system is giving you fits.
The problem is, why it is doing it is a little more difficult to figure out.
There is several GM Security lockout reset procedures on youtube that you might be able to see if it corrects the problem, but you are possibly looking at having to have the system scan with the correct scan tool to see why the security system is having problems.
It can also be a problem with the ignition switch itself or the connector to it.