I forgot to add that, for Time Patrolmen, as for the Time Traveler, time does not fly. They can always go back. Thus, in "Gibraltar Falls," Feliz would have drowned but Tom returns and pulls her out of the water in time. In Robert Heinlein's "By His Bootstraps," Bob Wilson tells Diktor to stop rushing him in and out of the Time Gate. Haste is unnecessary - but Diktor wants to keep Bob confused for a while.
When Everard, surrounded and fighting for his life, says in Temporal through a Patrol communicator, "Unattached Everard. Come immediately. Combat." (The Shield Of Time, p. 113), the battle is over. Knowing when and where their enemies were in the past, the Patrol can hit them at a precisely calculated time, making escape impossible - unless an Exaltationist is already seated on his timecycle.
For time travelers, it is not true that time flies but it is literally true that they have all the time in the world.