Maybe he finds it again every time.

It isn't the best translation because it can seem a bit confusing, but it is correct. Consider, for example, a laptop that is shared by two people, the teacher loses it, so the teacher lost their laptop.

a as a possessive can mean his, her or their, and the main way to distinguish which meaning is intended (other than simply context) is the intial mutation on the following word (is the word eclipsed, lenited, etc.), but since "r" cannot be lenited or eclipsed, you can only tell from context, and since a single sentence does not give much context, any of the three translations are possible.