Automation signal propagation through complex circuits

I have built a 7-bit shift register out of AND gates, NOT gates, Memory Toggles, and a Timer sensor. The Timer sensor sends a Green signal for 0.2s and a Red signal for 58.8s, with the goal being to clock the shift register once per minute. I have looped the output of the shift register back into its input so that a single bit/Green signal loops through it forever. It works flawlessly for the first few loops through the system, but eventually starts propagating further through the shift register. In some cases I have seen the bit get lost rather than duplicated.

I think the issue is based on the fact that the Automation circuits are really "clocked" on the game tick, not on my Timer sensor, and my in-game clock is really just enabling the circuitry for ~1 tick, but not exactly. This could possibly be solved with more complicated automation circuits.