I have heard stringers quote answers to this such as, “you should have your racket strung as many times in a year as you play in a week.” So, if you play three times per week then have your racket restrung three times a year.
I don’t necessarily subscribe to this answer because you may play for 3 hours each day. 9 hours of badminton a week is a lot and therefore you will certainly require more restrings.
If you play frequently, then pay attention to your racket. When you feel it’s lost something, maybe that’s the time for your restring. If you look closely at the strings then they may look a bit furry. That’s a definite sign of wear and they won’t have much life left.
Alternatively, you may notice that your strings are felling dead. You’re just not getting any power from the strings or your net shots are simply not happening. That’s a good time for a change.
All strings stretch. Therefore, if you had a racket strung at say 20 lbs, by the time you play with it I expect tension loss of around 10%. This is sometimes known as string creep. This loss of tension is normal and should be expected from any elasticated fibres. In this example your playing tension may be around 18lbs and the string will continue to lose more tension, but at a diminished rate over time.