Joel Kribel managed a 73 to finish four shots off the lead at 2-under-par 142 alongside Vic Wilk.
Thatcher, who fashioned a 66 over the difficult Bayonet Course layout during the opening round, was looking to build upon his early success.
'Let's see if we can't do this again,' said Thatcher.
The 25-year-old played the back nine first and didn't make a birdie until after he made the turn. He hit a wedge within inches at the par-5 first for birdie to move to 7-under but gave that shot back with a bogey at the very next hole.
Thatcher's problems continued with a bogey at the fourth but he countered with back-to-back birdies from the sixth to return to minus 7. However, a bogey at the par-3 eighth put him right back where he started.
'Even-par is still a pretty good score out here,' said Thatcher. 'I'm not that disappointed with the actual score part of it. I had a lot of things working for me today. I do think I had a chance to take it lower than I did. I just made some mental lapses and a few bad swings at the wrong time. It cost me.'
Thatcher, a rookie on the Buy.Com Tour this season, posted a top-10 finish at the third event of the year but has since struggled. Thatcher had missed the cut in each of his last six starts prior to this event.
Caron also started on the back nine and burst out of the gate with an eagle at the 10th. He added a birdie at the 11th but struggled with two bogeys over the next three holes to make the turn at minus 6.
The 30-year-old found trouble again with a bogey at the fifth but responded with a birdie at the par-3 sixth. Caron finished his round with a bogey at the ninth for a 72.
'This golf course will give you some breaks and not give you some,' said Caron. 'Today was okay. I didn't drive the ball as well as yesterday but 72 is still a good score out here. Anytime you can shoot 72 on this course, it's pretty good.'
Omar Uresti struggled with a 74 to finish five shots off the lead. He was joined by Mark Wurtz at 1-under-par 143. Aaron Baddeley was one shot further back at even-par 144.
The 36-hole cut fell at 6-over par 150 with 62 players qualifying for the weekend.
Full-field scores from the Bank of America Monterey Peninsula Classic