How often does it do it, like cut in and out continuously or a few seconds or minutes or days or ??
Speakers don't usually heal themselves, though at certain temperatures you could have the speaker voice coil shorting out. If the problem can be caught or reliably replicated when it's happening then you can measure for coil resistance with a multimeter (single digit ohms) and for signal coming from the radio (~20VAC meter scale) while playing music.
Did it seem to work better after you fixed it? How exactly did you fix it? The thing about those wires in the door jam is that if you find one frayed apart and just solder it back together at the break, you now have the rest of that wire which was also weakened from flexing, but now flexing even more because the solder joint creates a smaller flexible area of wire remaining.
In my opinion the better way to fix a fraying wire there is to insert a new piece of wire between the two broken ends, silicone insulated high strand count wire which is far more flexible than the factory wire was. You can usually find this type of wire sold in short(er) lengths from merchants catering to the R/C hobbyist on Amazon, ebay, local hobby shops, etc because this wire is commonly used as battery hookup wire. It's a shame Ford didn't use this type of wire in the first place.