Suicide, or "Kamikaze" Grunts were added in Halo 3, and can be nasty little buggers if you're not paying close attention to them. That said, they do not run indefinitely. Each difficulty increases the amount of time that a Grunt can run. Mind you, on easy this distance still isn't short, especially if they are close. Here's a breakdown of the times and rough distances for each difficulty.
It took about 18 seconds from ignition of the grenades to explosion. Grunt was moving the whole time, though some repeated movements were made where it looked like the AI couldn't decide which way to go.
Normal also took about 18 seconds from ignition to explosion. Two grunts ran at me this time, both exploded apart from each other and at roughly the same time. Distance didn't seem to be much different.
*Note: The grunts did not explode at the same time, but they were pretty close to one right after the other.
Heroic had an additional 6 seconds, bringing it up to a total of 24 seconds from ignition to explosion. That additional time adds a lot of distance and requires a lot of open space to run away from.
There was an additional 4 seconds in Legendary when compared to Heroic, bringing the final total up to 28 seconds. The distance covered here is very long for most any open stretch in Reach, and to run away, you will likely need to do a few circles (or jump on a platform, see below).
Grunts will blow their payload if they die, are too far away from you or if they are unable to reach you. This means that, if you have a jetpack or a platform to jump on, they will blow themselves up immediately. Also, a simple headshot will drop them quickly.