As mentioned by the other commenter, a lot of his drinking stories were told by his rivals or enemies during and after the War. McClellan in particular kept the rumor of Grant's drinking alive as Grant's victories in the West kept stacking up and McClellan was... uh... "struggling" in the East.
However, the modern view* is that the issue wasn't that Grant drank all the time, rather that when he did, he binged and basically blacked out. There were plenty of commanding officers that were literally drunk during battle, so it seems to me that at the time, the bigger taboo was being a lightweight. Most of this stemmed back to his days as a young officer stationed up in bumble fuck Oregon, where he was caught manning the payroll table while drunk. A young fellow officer, George McClellan, was visiting base that day and never forgot. Rather than accept a punishment, Grant resigned from the Army. This overreaction on his part led many to believe that it was more than just being tipsy at his desk (my take is that he missed his family dearly and this was the first half-decent reason to leave the Army and head home).
At one point during the Civil War, Lincoln sent someone to keep tabs on him because of the pervasive rumors. That reporter ended up being one of Grant's biggest defenders. By most accounts, when Grant did drink, it was during periods of extended inaction, he got shitfaced, but was up early the next morning without a hint of hangover. No one close to him ever reported (publicly or privately, including diary entries) that Grant had drank prior to or during any moment of importance during the war.
*My view on this is shaped by 3 biographies written in the last 10-15 years by excellent, objective historians: Jean Edward Smith, H.W. Brands, and Ron Chernow. I highly recommend any of them (or all of them if you're a nerd like me...).