AvatarNathan Richer

without looking at any pics of you sitting, i’m guessing that as you tire from long periods of sitting, your pelvis is rolling back into posterior tilt, causing lumbar flexion, and that probably puts pressure on the disc and creates pain. 

during activity, you may have good enough stability to maintain a spine/pelvis relationship to not have pain. but it comes back when you sit.
or you may think you have good sitting position but there is still something that is off, or the disc is sensitive to you being in that position.  skillful sitting is hard to master – we do it all the time but not many people sit correctly and can sit for long periods of time in that position.
might want to take a look at doing some hip flexion work, psoas gut smashing, hip openers.  good ol’ couch stretching is a good idea as well. any one of these tissues may be preventing your pelvis from rotating into a good position during sitting.