Cal, any number of the "activities" (blue locations on map) have timers. Genki's SERC, Insurance Fraud, for sure. But probably all of them do, as they pretty much all did in SR2.
Also, if there's a way you can... maybe be able to make a vehicle in your targeting reticle invincible? Would help on those missions where you have to protect a vehicle.
Thinking of the beginning mission where you have to protect Pierce with a rocket launcher from a helicopter (one of the first few missions). This mission can be rather difficult if you've aquired and upgraded the rocket launcher already due to the increased explosion radius and increased damage. Just a thought, if you can do that. Think it's also a side activity known as "Guardian Angel" or something like that.
can you get into the vehicle you are trying to protect? if so you can get into it and turn the option on. then leave it on and leave the vehicle and get into your own vehicle.
not sure about any other method right now, sorry
best,
Cal