bullfrog-807, I used to have the same problem on two of my old 29 LTD Classics. When the squelch was set and someone local or with loud swinging modulation would come in, the squelch would start clipping the modulation. That would make it sound like they are cutting out. I have never seen a fix for that particular problem posted on any other cb site or cb trick or mod site.
However, years ago I did solve my problem with some tinkering around. VR3 is the squelch adjustment in the radio. If you are not familiar with radio adjustments take it to a reputable cb shop. Unless you are confident that you can use a soldering iron to install one simple part, that may fixed this problem.
I am by no means a radio tech. This would be at your own risk if you open your radio up and do anything to change things.
One capacitor is all that's needed. Find a 25 volt 22 uF electrolytic capacitor.(the one's that look like a small can with two legs on them) They can be found in just about any scrap radio or electronic junk.
Find C147 (.039uF Mylar Cap.) located near the squelch adjustment VR3. If you can find the solder joints of C147 on the solder side of the pc board (that is the top side of the radio) solder the 22v.-22uF capacitor to C147.
As I have said, I've never seen a fix posted anywhere for this problem. The problem may actually may be the value of C147 itself. Haven't tried actually changing the part out. By adding the extra capacitor to the back side of the existing one did work for both of mine. This is actually changing the value of the part.
These were the older Cobra radios made in the 90's.
My newer ones don't have this problem.
If it is alright to post a link for the schematic and screen shot of the radios pcb, here it is. Hope this can help you and others out there that may have a similar problem.
http://www.cbtricks.com/radios/cobra/29ltd_29ltd_st_29wx_st/graphics/cobra_29ltd_sm.pdf