You should determine if the bass has a sustain issue or not by playing it cleanly through an amp, not distorted to death through a recording console. Go up and down the neck, note by note, and let the notes ring out completely. That will tell you if there is an issue inherent to the bass itself. You will almost certainly find a shortness of sustain on the G string between frets 5 and 8, unless you are playing something like a Modulus, Zon, or other carbon necked bass. Maybe play those notes first, and then start with open E so you know what a lack of sustain sounds like.
Take 5 minutes, do exactly that, and you'll find out if the issue is with the bass or somewhere else in your chain. There's no point in continuing to trouble shoot if you aren't taking steps to rule out individual components to your overall recorded sound.