It would help a lot if you would provide a little more information.
How old is "older" (they've been making them for more than 50 years)? What kind of Gravely is it? Do you know what engine is on it?
Here are some possibilities which may or may not apply to your machine.
After a short time, the engine is either (1) not getting enough fuel (or possibly too much), or (2) getting a weak or erratic spark.
You may be able to determine which is the problem by slowing the engine to idle when it starts sputtering. If the engine will then idle smoothly, then your problem is probably a fuel shortage. Otherwise it is probably electrical.
(1) The carburetor has a float chamber which holds a few ounces of fuel. A float in that chamber will shut off the fuel supply when the chamber contains a certain amount of fuel.
(a) If the float is worn or isn't floating properly, the level of the fuel will be wrong and the engine will not get the correct fuel/air mixture.
(b) If there is a fuel filter in the fuel line that is mostly plugged, there will be enough fuel in the chamber to keep the engine running for a little while, or at idle, but not under an extended load.
(c) If the machine has a fuel pump (for example, a riding mower), the pump may use a diaphragm driven by pulsing engine vacuum. If the diaphragm is worn out and leaking, the pump won't deliver enough fuel to the float chamber.
(2) Here are a couple of possibilities if you're getting a poor spark.
(a) Sometimes the coil (which generates the high voltage for the spark plug) can fail when it gets hot. The older walk-behind Gravely's (maybe 1975 and earlier?) used a magneto, and the coil is expensive (over $50). I have two Gravely's of that vintage, and have not had a problem with the coil failing, so think twice before throwing money into a new coil if you have one of those machines.
(b) If your "older" Gravely is new enough to have an electronic ignition, that too can fail when it gets hot. I have no experience with a Gravely with an electronic ignition, but I have replaced them on other machines.
If this doesn't help, post some more information about your machine and your problem.