No, don't let your DoTs drop. If Rupture is running out during KB, I will let Envenom drop for a bit if I need to - the important thing is to still hit Mutilates during the Envenom window, as those are double hits that can each apply a poison. A few white swings without an Envenom buff will not make a huge difference (white swings can miss anyway), but going Mut-Mut-Envenom without a buff is a big loss.
So, if I see Rupture is getting close to <7s while KB still has >7s (in other words, Rupture is refreshable, and I see that it needs to be refreshed before KB ends), I typically land a 4/5CP Envenom, immediately go Mut to 4/5, Rupture, and Mut to 4/5 again, all before the Envenom buff falls off. Then, I'll let the Envenom buff expire and Envenom again right at the end of SoT to clip it and re-apply Envenom.
It takes some practice but it becomes intuitive eventually. Basically, try to NEVER Mut without an Envenom buff if KB is running.
Here's an example of more or less what I'm talking about
:
https://streamable.com/og133. I refresh Rupture during KB and Envenom only falls off for ~0.5 seconds.