Check, double check and triple check all your connections. Especially anything that is crimped. Pay close attention to fuse holders, especially the ones that hold the glass tubular style fuses.
Check for corrosion on all the connectors. If it's corroded, stop and fix.
Check your battery. Could be your battery is getting weak. If the voltage takes a nosedive when you crank the engine, it may be time to replace the battery.
Length of the power feed is important, too. There is loss in all cable, and if you are using a long run with small cable, you may be experiencing enough voltage drop to create an issue when the engine is cranking.
As for where to ground, yeah, it can be contentious, but some newer cars are very specific about this. Check your owners manual. Some newer cars have sensors on the negative battery lead that watches how much current is flowing to/from the battery. The manual may tell you to not bypass this by connecting any accessories directly to the negative post. They'll want you to ground to the chassis. Which is a good thing to do anyway, especially close to the radio. Do not rely on the long negative power lead as the radio ground, nor the grounding from the antenna mount. Run a short strap from the radio chassis/ground point to the vehicle chassis.
If all those things check out, I'm willing to place a small wager that it's time to get a new battery….