The combination finished in the top 35 after last night's third qualifier at the Sha Tin equestrian venue in Hong Kong.
The seventh rider to go from a field of 51, Webby had to endure a three-hour wait to see if he had done enough on the challenging 13-obstacle track to be among the top 35 to advance to the finals.
With penalties carrying over from the first two qualifying rounds, Webby, 37, making his Olympic debut, doubled his tally of 12 coming into yesterday's round. A couple of unlucky close calls were not enough to stop the US-based Webby from squeezing into the final cut after placing 33rd.
With the heat and an energy-sapping three rounds taking its toll, Webby welcomed the two-day break his horse will enjoy as well as the prospect of all combinations starting with a clean slate on Thursday. The 15 combinations with the highest penalty counts will be culled after the first round on Thursday with the top 20 going on to jump-off for the medals.
"She's running out of gas a bit and just needs a couple of days to spark up a bit and refresh," Webby said of his mount.
"I knew my chances of progressing wouldn't be too bad because the field wasn't jumping super."
A dropped rail at the sixth, the first of the three doubles on the course, the merest of hoof touches on the tape at the water jump and tapping a block on the wall at 11 enough to dislodge it, left Webby with a three-round total of 24 penalties.
"They were pretty close calls but she was getting tired and lacked a little bit of spark tonight," Webby said.
"They were faults that she wouldn't normally have. It's been a tough few days and it's just catching up with her a bit."
Sitah has had little work in recent months after a long lay-off following emergency colic surgery in April. Webby, originally picked as reserve for the team, is thrilled with the mare's response and quick recovery in her short time back.
"I was really happy, she tried her heart out," he said.
"Obviously it didn't start off too great being the reserve but I knew I had a good horse. Then she got the opportunity to go and things have improved from there.
"I couldn't be more thrilled with how she's gone. She gave it everything and from what she's come from, with as little work as she's had, it's been pretty incredible."
Webby is New Zealand's lone competitor after Bruce Goodin, Sharn Wordley and Katie McVean failed to advance from the original field of 77 to last night's top 50. The New Zealand quartet were also bundled out of the first round of team's qualifying yesterday.
In the final of the team's event, the US broke Germany's stranglehold on the equestrian competition to pip Canada in a jump-off after both teams were on equal points after the regular competition. Norway picked up the bronze.