I think you only need to look at the games they give away to see why it's profitable. The games either have an upcoming sequel to which a PS+ giveaway is a great advertisement for the sequel, or a lot of DLC which will inevitably be bought. Especially as most games have the DLC on sale in their give away month. I doubt Sony is paying the third parties much (if anything) to be a PS+ game of the month - as it results in that game making more money then it would have probably by a large amount (Just look how succesful the humble indie bundle is...). That is of course done via DLC sales AND extra PSN sales to normal customers due to the 'priority' PS store placement.
I think the service also helps keeping the PS store active. A big problem with these online stores is people often have no real point in 'browsing' them beyond when they KNOW a game they want is coming out. PS+ gets all its users visiting the store weekly and paying attention to sales, and new game release. I'd imagine it's a huge factor in PS store activity.
I expect the service to fully mature for the PS4 and offer an even more complete feature set, as well as even better giveaways. There arn't many things I feel Sony 'gets' nowadays but this is one of the few things I think they've absolutely nailed and it really is starting to make Xbox live and XBLA look archaic - albeit as a non-Xbox owner I can only really base that on what my friends have said to me (Who are Xbox players).