Hello,
I have a Nishiki Tri-A frame built with modern components and my handlebar rotates forward when I put more weight on tops.
It happened recently when I found a snow/ice patch on a trail and found myself balancing and to get through, but walked most of the parts .
And recently when I climbed some standing up.
I can loosen and tight back to the position I want, but this keeps happening few times now.
The size of quill stem and handlebar are for 25.4mm, so it is not an unmatched size issue.
Any suggestion/opinions are welcome.

If you're tightening the bolt with seems like (or measures as) sufficient torque but the handlebar slips, pull the stem bolt and grease the threads on it and the stem and retighten.

If the stem is nearly fully closing around the bar (i.e., if the slot is nearly closed), cut a shim from a soda can and insert it between the bar and stem. If the aluminum from the soda can is too thick, use aluminum foil.

In addition to the good advice already given you can rough sand the clamping section of the bar and use carbon gripper paste too.

The bar clamp of the stem is key here if it is closing all the way and not getting tight enough, something is amiss.

Not all marked parts are always what or as they seem, someone could have clearanced the bar clamp of the stem and the bar has probably been ground down from slipping so won't hold, too small anymore.

One or both could have been mismarked or incorrectly sized but sounds like you may have measured already.

Shims can be fussy but often do the trick.

And in addition to merziac's good advice, look closely at the bar and stem to check for scars or cracks. If you see any, it would be best to replace both parts. Drop bars and stems in 25.4 would be old tech at this point, and yours are probably ready to be replaced anyway if the bike was ridden a decent amount over the years.

This

As a lifelong mech/tech/hack including pro on cars I always assume this goes without saying and forget that anybody that hasn't done this sort of thing for a living doesn't.

And the internet doesn't help as a first line of defense without skill and experience to back it up.

I've been around a while, Ridden several bars to breaking. Bars break. Just a matter of time. High quality ones ridden not too hard and not crashed, sometimes a very long time. But crashes, strong riders ... can mean even the good ones have been stressed and doomed to a much shorter life.

The older the bar, the smaller the diameter and the thicker the wall thickness, the more likely that the failure when it happens will be "gentle". I had a late '60s GB bar (a lot of miles, how hard unknown) bend 30 degrees at the outer edge of the reinforcing sleeve when I dropped the front wheel into a winter pothole. It was 5 miles later when I looked down and noticed. Rode another 5 miles to my training partner's house, checked the train schedule, a mile to the station and another home. Recently I was riding to the local velodrome 2 miles from my house when I chased down a sound to a tiny crack in the same area on a modern, nice set of bars. Rode gingerly (uphill) to the track. Put in a word to the announcer to please ask if anyone was going home in my direction. No way was I going down that hill to the stop sign!

Thank you all for the detailed information/instructions.
Will look if I have some gap in there I can fill with aluminum foil and check all the safety tips mentioned.
Fun for weekend

Greasing the bolt is a great idea, I always start with that. And using a good-quality and long-handled Allen wrench!

Making sure that the tip of the bolt isn't perhaps bottoming out in the bottom of the hole can be done by adding a "thin" washer, testing for improvement.

In the days of mostly lightweight 26mm bars, it was not uncommon to see handlebars having been subtly re-shaped by the clamp, such that having slipped once, they would forever slip down to the position defined by the deformation.
It's much less common to come across 25.4mm bars having been deformed by the stem clamp, because the bars tend to be a little thicker.

Removing any lubricant that may have crept into the clamping surfaces might make a difference.

I had a set of Cinelli bars and stem that would slip slightly. I greased the binder bolt threads, torqued it to Cinelli's specs. and it stlll slipped. Someone recommended putting blue Loctite between the bars and stem. I tried it and they haven't slipped since.