Actually it doesn't quite work like advertised
The Archer has an autoloader and modular charges where every charge is the same. It has a magazine that holds 21 rounds. If it fires at the specified 8 rds per minute, it's out of ammunition in just over 2.5 minutes. The reloading of the magazine has to be done manually. The older ammo truck has a small platform that allows the ammo handlers to open the magazine hatches, put in more rounds and mod charges and send it back into action. I haven't seen any actual figures about how long that reload takes but a partial video I once saw of it gave me the idea it could take 15 to 20 minutes from once the gun actually arrives at the reload truck. So I'd say from coming out of action to getting back into action for the next 21 rounds is probably a 1/2 hour + turnaround.
The M109 on the other hand carries 28 to 36 rounds plus charges depending on model while the M992 carries 93 rounds plus charges which can be modular or variable. Generally the M992 is paired with a gun and deploys right behind it. There is a mechanical feeder that can transfer the rounds from the M992 to the M109 but most crews just back the two vehicles to each other and do the transfer by hand. The one thing is that it's a continuous process. There is no autoloader in the M109 (yet) so loading rounds in the turret and transfer of rounds to the turret can happen concurrently. So technically at 3 rounds per minute, the M109 with its associated M992 could keep firing continuously for roughly 40 minutes.
Assuming the Archer fired at the same rate of 3 rounds a minute it could fire for only up to 7 minutes continuously before needing to recharge it's magazine. If the Archer had a better protected limber vehicle than a soft skinned seacan then its magazine recharge time could be dropped down to just the 15 to 20 minutes.
Just a point, I've seen M109s fire faster than 3 rounds per minute. 5 is quite possible but the rammer and need to load a primer with each round limits it beyond that. The M777 is rated a 2 rounds per minute normal, 4 rounds per minute rapid. Here's a video of a Canadian crew in Afghanistan putting 9 rounds downrange in 1 minute and 25 seconds or 6 rounds per minute. (as an aside there is some improper gun drill here that speeds up the mission but could lead to damaging some components on the gun) When you do not have autoloaders the rate of fire and how long you can sustain it is very much governed by the crews ability to prepare the ammo for firing and their exhaustion.
There is an ongoing project for an autoloader for the M1299 which may also end up in the M109 which will change everything.
One more complicating factor: not all rounds are the same. There will be some illuminating, some smoke, some RAP, and the bulk HE with a multifunction fuze. That limits on-board rounds availability for a given mission9s) as well.