You really ought to try to get to the bottom of this. If your vet is stumped, maybe he or she can refer you to a board-certified veterinary internal medicine specialist?
From the little I've read, 3x normal typically is the line where they start trying to investigate to find a cause, or persistently 2x normal. There are a LOT of potential causes of liver injury/liver disease though, so it's a detective exercise to get to the root cause. Your vet may need to hear that you want to find answers as to cause, even though it's going to cost some money to do that.
Exposure to toxins is apparently a big one to look into -- and the list of things that are hepatoxins is large, but that's a task you can work on for your vet. It apparently includes landscaping (esp. sago palm), blue green algae (common in warm, stagnant water in some parts of the US),
Amanita mushrooms, aflatoxins (common in grains, and sometimes found in some kibble), heavy metals, xylitol or chlorinated compounds (pool water would be a suspect here). The list of suspects also includes some RX veterinary drugs (ketoconazole, azathioprine, carprofen, lomustine, acetaminophen, mitotane, phenobarbital and more). You also have supplements and herbal remedies implicated as suspects (with herbal teas, pennyroyal oil and comfrey being the biggest suspects). My list here is just copied from an article mentioning "common" liver toxins -- but you might haven an uncommon one. The ASPCA has a list of poisonous landscaping plants for dogs, so I would go through and, check off what plants you know are around that might be problems:
https://www.aspca.org/pet-care/animal-poison-control/toxic-and-non-toxic-plants
I would then evaluate home, lifestyle, and everything the dog could ingest -- literally walking the property where the dog hangs out, looking for things that might be getting nibbled regularly on that are on the poisonous plant list.
Lepto and canine adenovirus-1 can also be root causes of liver injury. Then there are major disease states of other organs that show up with elevated liver enzymes -- diabetes mellitus, hyperadrenocorticism, hypothyroidism or hyperadrenocorticis are all possibilities. You might be getting an "early warning" about some other treatable disease state, and you don't want to ignore that early warning, right?
So...lots to investigate. Some imaging is probably in your future, and maybe cytology.
This vet-oriented article goes into a lot of detail -- it's long, but it will help you be a well-informed consumer with your vet for discussing next steps:
http://veterinarymedicine.dvm360.com/canine-liver-enzymes-so-many-questions?pageID=1
