I also have the HP5510 and am on 10.8.2 Mountain Lion and no problems for ages, and just done a test print to make sure and all is ok.
I did, early on in my iMac/HP "life", have a problem where the iMac, seemingly, refused point blank to see or print when all had been fine a few days before. I couldn't make it work at all, and even got a friend who runs his own IT business to take the printer in to see if he could make it work. What it turned out to need was a reset of my BT Homehub. Did that, restarted everything else and all has been hunky-dory since.
Maybe worth you reseting your hub....?
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