The limitations, as we know it:
Fuel. The infamous rocket equation means we get roughly a few times more fuel for every km/s delta-v budget.
#1 is why we avoid braking by rocket engines. When we reach Mars, we need to be almost at the speed of Mars and then brake in its atmosphere.
If we go faster, Mars' tiny atmosphere cannot brake us enough. And even if it does, the heat and acceleration will impose quite a requirement on the payload. More protection means more mass, i.e. more fuel in the first place. And even with all the possible protection, the atmosphere can do only so much and then we risk flying back into space or reaching the surface at rather unpleasant speed.
So we should brake by rocket engines, expending our precious delta-v budget. The rocket equation says we need the fuel for braking and even more fuel to bring the fuel for braking to the place where we need to brake.
Acceleration - humans can survive 1g for quite a while, ~3g for short time (like tens of minutes) and 10g feels and hurts like a car crash. Any scientific payload is hardly 10g-safe. We can probably make it survive 10g, but it will get heavier - see the rocket equation again.
Ah, I forgot - a more powerful rocket will have to withstand its own acceleration, i.e. will be heavier and will carry less fuel per unit of mass. Rocket equation all the way...
So no, unless we make a great leap forward in the rocket science (and it IS a rocket science) we are not going to Mars any faster.
What we can do now is to make the travel e.g. 2 weeks shorter for like double the expense.
So the main risk is quickly going over budget for no apparent gain.
The same factors say we don't save much if we go much slower either. We can probably use a gravity assisted acceleration near the Moon at the price of month or two more and at least 2 more burns.
And yes, engine starts are limited resource as well.