2002 Chevy Suburban Voltage shut off when starting

Yes the fusable link if no good will shut down all power to the vehicle, but once a fusible link is burns it is not intermittent, so I don't think that's your problem, I believe you have a bad ignition switch, when it happens again try wiggling the ignition switch up and down back and forth and see if that restores your power let me know what happened.

Can you please explain to me what the ignition switch assembly looks like? I want to make sure were talking about the same thing, not the ignition switch that the key go's in but the ignition switch assembly That activates power to everything. Okay now we are going somewhere else with a "strong fuel smell" do you have an engine light on? There may be several reasons why it's hard to start:
1. Check exhaust system for restrictions, such as damaged or collapsed pipe muffler or catalytic converter also it may be A plugged up catalytic converter.
2. Check ignition system for bare or shorted spark plug wires, loose ignition connections, check for shorts by Misting plug wires with water.
3. Check ignition system for faulty ground.
4. Check the color of the spark if it's yellow? Or blue?
5. Remove a couple of sparkplug and check them for being fuel fouled, properly gaped, wore out, ect.
6. There is another 20 things to check too much for me to list why don't you go to your local library and get a manual and troubleshoot, I believe if it's not ignition it would have to be fuel problems, I would like to help you but you're not being specific enough, write me back and tell me more and don't hold anything back.