That's my rotation as well and I, too, begin to feel the mana pinch in longer fights.
What I've taken to doing is slightly throttling back on how rapidly I cast. For example, I'll wait and see if Missile Barrage procs after I've cast the third Arcane Blast instead of as usual, which is to follow with another three Arcane Blasts whether or not it procs on the last one because by the time I see that it has proced I'm already casting the first of the next three Arcane Blasts. Missile Barrage remains castable for 15 seconds and casting three Arcane Blasts takes seven or eight seconds. Plenty of time!
Anyway, waiting that extra bit only takes a second and over the course of the fight can help keep mana going just a bit longer.