Can I gunzerk forever?

It is possible to gunzerk forever, as long as you have a target to shoot at (like a raid boss or arena waves).

To do that, you need two skills and a certain special class mod. You need:

• Level 5 Get Some reduces Gunzerking cooldown by 3 seconds when you shoot an enemy, every 3 seconds, even in Gunzerking.
• Level 11 Last Longer increases your Gunzerking duration to 53 seconds. For that, you need...
• Blue-rarity Two Gun Berserker of at least level 50 - it will give you +6 to Last Longer (note that purple-rarity mod gives +5/4/4, so blue is preferable for a single skill).

Cooldown is 42 seconds, so gunzerking for 53 (or even 50, with +5) gives you enough time to burn through the cooldown even before it starts, so as soon as your Gunzerking ends, you just pop it again, with added bonus of +50% health and instant reload!

If that guy in your game did not shoot someone at least most of the time (or surgically once every few seconds :-) ), he did cheat.

It's theoretically possible due to the skill where killing an enemy gives you a couple seconds more Gunzerking time, but if the ability lasted for more than 30 seconds with no enemies around the character was almost certainly cheating. It's noteworthy that in just about any normal playthrough you'll repeatedly hit brief lulls that are long enough and free enough of enemies that will cause Gunzerking to end even with these skills.

There are ways to increase Gunzerking time without killing enemies but it will eventually run out in a minute or so without killing enemies even with the best skills. There is no "infinite gunzerking" skill/combo of skills without manipulating the game or your character (for example to give yourself a million points in Gunzerking duration.)