Tear trough filler only possible three times a lifetime?

Hyaluronic acid fillers do not cause scarring. Filler injections can be repeated as many times as you want without worry.

What you have, allegedly, been told is incorrect. 
I should add that tear trough-correction is frequently more than simple volumization of the tear trough itself - the treating physician needs to understand why the depression has evolved. On the one hand, you must be wary of over-correction (or even 100% correction) with hygroscopic fillers, and on the other extreme, surgical excision of the fat pads under the eyes may not be what is needed at that stage. 
In my opinion, a combination of Restylane Lyft (formerly known as Restylane Perlane) and Belotero Balance (formerly known as Esthélis) are good for this area. I would absolutely 'NOT' use any of Allergan's Vycross fillers (esp. Volbella) around the eyes. 
To conclude, there is no limit to the number of episodes of treatment of tear troughs with hyaluronate-based fillers, but I counsel you to go to a doctor who has experience in this area.