When love comes into play there is an object in mind but it gives itself freely without expectation of any energy in return. Pure love would not have bias of any object(like you said "without attachment"), so there are many objects, and would give its energy freely till it depleted itself.
This is a good point. I have thought much more on this since the OP and feel that love doesn't deplete if focus on the source i.g. God/The Divine. From a non-dual Dharmic or Pantheist view this love comes form "us" anyway.
We could take a more 'scientific' explanation that because energy just dissipates, if energy is focused back at its source rather than at any object then it will just be returned. It would be recycled: God loves you - you love God - God loves you ad infinitum