The England squad member went down 4&3 to Scottish Walker Cup player Ewen Ferguson after winning his way through his second-round match in the morning.
He had fought back from two down to triumph 2&1 against Switzerland's Marco Iten, the man who had defeated Bower's Yorkshire team-mate Dan Brown (Masham) in the previous round.
But Bearsden's Ferguson, who two years ago became the first player to hold the British Boys' title plus the Scottish Boys match play and Scottish Boys stroke play titles at the same time, proved too strong on the day.
Bower, who won two titles while in South Africa earlier this year touring with England, lost the first hole to Ferguson's birdie, but squared immediately with a par at the next.
Bogeys at four and six left the Yorkshireman two down, but the gap halved instantly when the Scot bogeyed the par-3 seventh.
The roller-coaster nature of the match continued when Ferguson pulled two clear again at the eighth and a second bogey at a par-3 by Bower put him three holes adrift after 11.
Any momentum Bower gained by eagling the 579-yard par-5 to get back to two down dissipated when he had to concede the next, and a birdie at 14 by Ferguson gave him a four-hole advantage.
The game was up for last year's English men's semi-finalist when he could not better Ferguson's par at the 15th, but it was still a commendable performance coming on the back of his victories in the Gauteng North Amateur and the Southern Cape Open.
Hertfordshire’s Jackie Foster came from four shots back to win the English senior women’s stroke play championship at Burnham Beeches, in Buckinghamshire, as Richmond’s Karen Jobling faded to 13th.
Jobling was second, three shots behind the leader Sue Spencer (Whittington Heath), going into the final round.
But after a fine start she started to miss too many fairways and added a closing 85 to her earlier efforts of 76 75. Foster shot 79 73 77.