On the 17th, Fox found the water hazard from the tee, which cost him a shot.
At five-under, Fox sits nine shots off the pace set by Englishman Matt Fitzpatrick, who followed up a six-under opening round with an eight-under round on Saturday.
Fitzpatrick, who was tied with Fox in fourth after round one, counted eight birdies without a blemish in his second round to take the outright lead at 14-under. He sits one shot ahead of Norwegian Viktor Hovland, with American Harris English sitting in third, three shots further back.
World No 1 Scottie Scheffler carded a four-under round to move to seven-under for the tournament and into a share of 14th.
Defending champion Justin Thomas remains at the foot of the leaderboard after a four-over second round put him at nine-over for the tournament.
The RBC Heritage has a total prize purse of US$20 million ($34m), with the winner taking home US$3.6m.
Fox made a strong start to the PGA Tour season with four straight top-25 finishes, including a seventh at The Genesis Invitational, before kidney stones forced him to withdraw from The Players Championship last month.
That stalled his form, with back-to-back missed cuts at the Houston Open and the Masters. Being a signature event with a smaller field of 82 players, the RBC Heritage doesn’t have a cut.
Hilton Head Island is 240km south from where Fox won his maiden PGA Tour event at the Myrtle Beach Classic last year.
“It’s a nice part of the world to play. Last time I was here in 2023 I had pneumonia, so I don’t have great memories of this place but I’ve certainly changed them a lot this week. Really enjoying the week in Hilton Head. Got my family here, got my in-laws here. The kids are having a great time and that makes it easier to play well on the golf course,” Fox said after his opening round.
“It’s just a nice change in general coming down here. Last week, it’s tough, it’s stressful and then you come down here and while the golf course might be tricky it’s just a fun week to be part of. Everyone brings their families and has a great time and we’re certainly enjoying that this week.”