Under-eye filler softens a hollow for a stretch of time, and then the hollow comes back. This page covers how long that stretch usually runs and what changes it.
One to two years is the planning range
Cleveland Clinic says fillers can last for a couple of years but vary for every person based on their anatomy and the kind of filler used.
The same source adds that, on average, you may need to get injections every one to two years to maintain the full effect of the filler.
Why your own timeline can differ
Two things move the date: your anatomy and the kind of filler placed. Neither one is a number you can read off a chart.
The product choice is worth settling before the appointment. Nebraska Medicine's article on which dermal filler is best for marionette lines, lips and tear troughs is a good companion read.
What to do when hollows start to show
Ask your provider which filler they used and what timeline they expect for your anatomy. That answer is more useful than any average.
Before a repeat visit, the FDA's dos and don'ts for dermal fillers are worth a read. A systematic review of adverse events reported after hyaluronic acid filler injections to the face and a systematic literature review on safety and complications of dermal fillers cover the safety side.
The day the hollow reappears
The answer changes the day the hollow reappears. That is the moment to ask whether a repeat session fits, and the one-to-two-year range is the window to plan around.