The reasons for replacing a removable retainer are: breakage, loss, ageing of the material with a change in colour, or your orthodontist advising you to replace it at set intervals. If the piece that has broken off is small and at the back teeth, it is usually not urgent, but it is advisable to replace the retainer within a week or two.
This answer is for general information. Your own case needs an examination by an orthodontist.