George,
1. Replace the coax.
2. Use RG-8X marine coax. It is only a tiny bit more expensive than RG-58, and is just about the same diameter...a tiny fraction larger. Note that this is NOT the same larger diameter as RG-8 or RG-213.
Here's a good source for the coax:
http://www.therfc.com/
What you want is RG-8X marine (C8X) @ $ 0.38 per foot.
You also want good quality UHF connectors (PL-259) with reducers (UG-176/AG) for RG-8X coax. Amphenol's are good; I've found the imported silver ones they carry to be of high quality, too. It's worth a call to ask them about the current best connectors, since all connectors are NOT created equal.
Bill