I noticed this during todays interval session inside on the trainer (it's raining out). In the latter half of my 10min intervals, I would become aware of my legs burning, and my heart rate would drop a few beats. Noticing this, I increased my effort and got my heart rate back up.
This is all a mental challenge. It's not that I wasn't working through the pain with the lower HR, it's that I was focusing on the pain/discomfort instead of maintaining my level of effort. Now that I'm aware of this, I can work on fixing it.
I also know that I need to pay more attention to my resting HR in the morning. On some rides, I'm not sure if I'm "tired" or just being lazy when I'm having trouble getting the job done on a hard training ride. Maybe there is more to it than resting HR, also. Something to look into might be RestWise, which Rebecca Rusch uses. Based on my limited understanding of this system, it takes a more holistic approach to recovery, and determining ones state of recovery.