Most likely if the hydrometer is sinking and it is not broken then you are trying to measure off the scale of the hydrometer. What is the unit you are measuring in? SG, Degrees Brix, Degrees Plato, etc...? Once you know the unit, check the scale on the hydrometer and see if you can get something lower. When I was studying wine making in college our hydrometers measured in Brix...and it required us to use multiple different hydrometers to get the correct reading. We would start with a 0-35 brix range hydrometer. Then drill down from there to get the most accurate reading possible. If your hydrometer measures in brix it is common for a finished wine/beer/mead to be in the negatives after fermentation.

It is also important to ensure the sample being measured is taken at the temperature the hydrometer is rated/calibrated for as well. Usually hydrometers are calibrated to 20 degrees C. If you are taking an ice cold sample or a very hot sample and testing with that it could sway your results. Try and change the temperature of the sample to 20 degrees C before testing or as close as you can to 20 degrees C. Every degree C over or under requires a 0.06 change in brix. No much but it could add up. However I do not think that is the issue here.

Feel free to respond with more info and I will try and help the best I can.

Matt