Here is a list of all of my Mods in case it's needed.

Issue:

• ~100km, MechJeb 2 auto-pilot status changes from "Gravity Turn" to "Fine-Tuning Apoapsis".
• MechJeb 2 throttles down to 0.
• Liquid Engine thruster flames out.
• Remaining ignitions are 0.
• Lost Δv due to early engine flameout.
• Disabling autopilot leads to engine cut-off instead of just leaving throttle where it currently is.

I know I should design my rocket such that, by MECO, I no longer need the first stage. However, I'm not there yet. I still have more to learn about orbital mechanics.

Any ideas on what to do other than forgo autopilot or find another engine configuration?

The MJ settings panel should have a RSS option. When it is activated it should prevent engine shutdown when using the ascent AP.
It is not perfect but I did not have the time to work on a better solution so far.