Dont know if the cover directly contributes but by leaving the cover in place, you are less likely to check and wash-down the bats so corrosion has more time to collect. If your cables are corroding, it generally means that you bats are gassing due to age or charger/inverter issues. Lots of info on bats and bat maintenance on this site--do a search. I threw away the cover years ago and I literally hose down/wash off the bats everytime I was the coach. Some folks swear by putting 2-4 oz of mineral oil in each cell of the bats to minimize gassing. Again, if you are getting lots of corrosion on your cables, you need to check condition of bats and the charging sources.
2003 40' MDTS
Garden Ridge, Texas