I've been operating under the assumption that you can only reroll each die one time. A friend of mine made a "power build" he calls the Bill Murray build that focuses on repeatedly rerolling things until he succeeds, and I'm trying to find the specific reroll limit rule. If it doesn't exist, I'm never going to *not* have a double-bladed scimitar with Great Weapon Master, because I get to reroll 2d4 until both dice have higher than a 2, which eliminates every damage option except 6, 7, or 8 xD

This roll does not exist, but great weapon master has no mention of rerolling dice.

All abilities that allow a reroll will tell you how they work. Great Weapon Fighting for example has this:

When you roll a 1 or 2 on a damage die for an attack you make with a melee weapon that you are wielding with two hands, you can reroll the die and must use the new roll, even if the new roll is a 1 or a 2.

Most of them work like that. They say you can reroll but must use the new one.

Quote from Jeagan >>

I've been operating under the assumption that you can only reroll each die one time. A friend of mine made a "power build" he calls the Bill Murray build that focuses on repeatedly rerolling things until he succeeds, and I'm trying to find the specific reroll limit rule. If it doesn't exist, I'm never going to *not* have a double-bladed scimitar with Great Weapon Master, because I get to reroll 2d4 until both dice have higher than a 2, which eliminates every damage option except 6, 7, or 8 xD

As far as I know there is no such rule that would allow this to happen (at least RAW - homebrew could be different). In this case, it sounds like someone misreading the Great Weapon Fighting style that Emmber cited. In that case, the character gets ONE reroll of any die that isn't a 1 or 2 but MUST use the re-roll. This fighting style does have the biggest impact for a 2d4 weapon since you might get to reroll two die and they are small ones so the odds are the total will improve. Great Weapon Fighting requires a weapon that you wield with two hands so a double bladed scimitar qualifies.

However, the Great Weapon Master feat, which gives a bonus action attack on a crit or kill and allows the character to take -5 to hit in exchange for +10 damage requires the use of a HEAVY weapon. This feat can't be used with a double bladed scimitar since the weapon is not heavy.

 Which rule was your friend using to re-roll dice?

With DMs that use the ruling that 1s are an automatic fail, halflings, who have an ability to reroll 1s, have an immediately increased value. 

Add the lucky feat to fill in gaps and your rogue/bard with multiple expertise may be unlikely to miss a skill check.

divine soul sorcerers can add a d4 to a failed roll of choice.  

lev 6 star druids can rig rolls with cosmic omens.

Quote from GergKyae >>

With DMs that use the ruling that 1s are an automatic fail, halflings, who have an ability to reroll 1s, have an immediately increased value. 

Add the lucky feat to fill in gaps and your rogue/bard with multiple expertise may be unlikely to miss a skill check.

divine soul sorcerers can add a d4 to a failed roll of choice.  

lev 6 star druids can rig rolls with cosmic omens.

You realize that none of these are relevant to the OPs comments that were specifically referring to re-rolling the damage dice of a weapon? There are, of course, a number of ways to reroll other dice but in this case the OPs friend was rerolling d4 damage dice on a double bladed scimitar to ensure a minimum damage of 6 and maximum of 8.

In addition, none of these allow for unlimited re-rolling of dice. Even the halfling has to accept a 1 if it turns up on a reroll.

When you reroll a dice you must keep the new result even if is worse,

Quote from AshantiTouree >>

When you reroll a dice you must keep the new result even if is worse,

Only if it tells you to. Some say you can use the old roll if you want - like the Savage Attacker Feat.

The OP was asking about if there was a general rule limiting how re-rolling works. The OP described a player using a build they called the Bill Murray build and they used re-rolling to achieve success. The re-rolling weapon damage repeatedly and using a double bladed Scimitar was an example OP came up with.

The context I have heard of the Bill Murray build in is a Zee Bashew video. In that video the build was a Halfling Divination Wizard with the Lucky feat.

To answer the OP's question: No, there is no rule generally limiting how often a roll can be re-rolled. Being able to re-roll is an exception and each feature, feat, spell, etc has its own set of limitations and restrictions.

Quote from Fangeye >>

To answer the OP's question: No, there is no rule generally limiting how often a roll can be re-rolled. Being able to re-roll is an exception and each feature, feat, spell, etc has its own set of limitations and restrictions.

While it's not a general rule, as others pointed out re-roll features usually have some form of limitation; the common ones are that you must either use the second result (even if it's worse) or you must choose one of the two results to use.

To my knowledge there are no re-roll abilities that allow you to keep re-rolling, as all of the abilities that I am aware of have one of these types of limits (or something similar).

So yeah, there is no "re-roll once" as a general rule, but unless I'm forgetting some specific examples (very possible) you still can't re-roll more than once. I know that games like Warhammer used to have a re-roll once rule though, perhaps that's where the confusion is coming from?