Embedded real-time software design carefully budgets the available CPU for the worst case. It would be deeply disturbing if the problem came from that direction, so I'm going to go out on a limb and guess that that's not it. Those programs tend to be extremely static in the sense that tasks/data do not arrive ramdomly or with variable rates, but everything is done on preallocated resources. All the fancy features of scheduling are dispensed with in favor of extreme predictability.
Frankly, if this is the case, as a software engineer, I would be appalled. This is Real-time Systems 1.01.