Climbing balance at slow speeds is affected by two things, and one of those two things affects the other.
1. Skillset: aka your proficiency at balancing at slow speeds, this is different for everyone, and not everyone has equal potential.
2. Fatigue: the more tired you are, the less of your potential skillset you can draw from.
Practice will help with #1, endurance training and planning for those effort ahead will help with #2
It should also be noted because of #2 slow speed balancing on the flat is not reflective of balancing on a steep climb
yesterday I spent 90 mins of a 2 hour climb under at 3-4 mph and a cadence of in the 40's. I'm out of shape which is making it harder than it use to be but that is my balance speed limit. It's only 8% average grade but it's 9 miles long so you plan to start slow and finish, or you don't finish.
Anyone who can ride a V20 or C40 with no hands like
@Jim Parker can may be able to go even slower.
View attachment 19259
Here's a link to the end of that same climb but years ago when I was in shape. The video doesn't show power data but I'm holding around 400 watts to maintain that 5 mph in the video. You can see my balance degrade as my HR rises and you can hear the tire break loose over some of the cracks in the road.