Priority inversion in a real-time control loop

On a robot's microcontroller you run three tasks under a fixed-priority preemptive RTOS: a high-priority motor-control task $H$, a medium-priority telemetry task $M$, and a low-priority logging task $L$. Both $H$ and $L$ access a shared SPI bus guarded by the same mutex. You observe that $H$ occasionally misses its deadline even though the CPU is far from fully loaded. Explain the mechanism causing this, why $M$ makes it worse, and how you would fix it. Also state one way you would detect or measure the problem on real hardware.