This alone might not have caused it. (Skype did fine under eBay management, although I'm sure not to its full potential, as illustrated by recent events)
However, the eBay horror stories of people getting screwed over and the various facilities supposed to protect them failing miserably usually include PayPal in some way. PayPal has become known as the payment processor used on eBay, and not much else, and with eBay's reputation these days, that's not a good thing.
In fairness, the PayPal arm of the company seems to be just as much to blame for eBay's reputation as a scam haven as the rest of eBay.
It's kind of funny, PayPal was a buyout that had obvious strategic benefits for eBay's core business and has ended up as a disaster for PayPal. Buying Skype was a rather odd decision but didn't seem to prevent Skype from being a success.
Indirectly, yes, I think that was a problem - by buying PayPal and closing their own payment service ("BillPoint"?) they ensured PayPal never had to worry about competition again.
and not to mention completely blocking Google Payments from having any part in ebay auctions, and shutting down the excellent Western Union Auction Payments service, where the buyer pays the fee to send the payment, and ebay can't double dip in the fees (charging the seller a fee for the final value and then charging the seller a fee to receive payment through paypal).