You're talking about using the Resume button on the download/search window & also the Force Resume function. The latter has a bad reputation for not always continueing the downlds from where they left off.

Since you have another issue also with the new version, there might be something else that's upset the balance. Did you do a SAFE Boot & Repair Permissions ? Perhaps you should make a note of all your LW settings, then close LW. Then trash your LW Preferences folder found here: /Users/your_username/Library/Preferences/LimeWire