If the sound is fading out very quickly with low volume, you could adjust the pickup height closer to the strings and see if that helpd...
If the notes are abruptly stopping, there's a better chance that it's a "fret-out" issue. This was most commonly an issue with vintage Stratocasters... it was caused by the 8 and 9.5" radius fretboards of their 50's and early 60's strats being so round that once you bent a note far enough the string would actually make contact with a fret closer to the bridge and either buzz or completely kill the note. Hence the name, fret out - And the birth of 10 and 12 inch radius fretboards...
The other causes of fret out can be high frets, a raised heel, or simply poorly set up action.
High frets can be examined by taking something with a 3 inch (or so) straight edge and laying it along the frets the way a string would and make sure the frets are all the same height. Moisture in the fret slots can loosen the seat of the fret and over time swelling of the wood can push frets out of the slot...
A raised heel happens when a fretboard or neck starts to warp. You can sight your neck by holding it at eye level and looking down the top edge of the fretboard from the bridge down to the neck then doing the same for the bottom edge. Both sides should have the same shape. Ideally a guitar should be set up so the neck has a very slight curvature to it. This is called "relief". If you notice that the heel of the neck is raised and the neck seems to bow down then back up to the headstock, you could have an issue. Newer strats have an adjustment in the neck plate that allows you to adjust the neck angle to compensate for this...
Lastly, your action and set up could simply be the issue. Have you changed to a lighter guage string than you normally use? Check to see if your action is set too low... Often, the compensation with low action is bending range.
