Does setting the weight back to zero each time prolong the life of a balance beam scale?

you mean one that's functional like a steelyard http://en.wikipedia.org/wiki/Steelyard_balance but with two sliding weights of different sizes on different scales?

In theory the metal might creep (bend a little permanently ) under load but if the beam is substantial and made of suitable material that shouldn't happen/have negligible effect. Steel might bend a tiny bit at first- but unless overloaded it'll stop bending after a while http://en.wikipedia.org/wiki/Work_hardening

There's always the same force acting down on the pivot, so that might seem to have negligible effect, but remember when the weight being measured is removed the arm will drop. if it's jarred that could damage the bearing/pivot, If left the bearing could be distorted. Again can't see it making that much difference except for a VERY accurate scale, for tiny weights .

It is preferable that the weight be removed. It is known that metal is subject to long term structural variations due to endurance of a weight. If a long thin wire is hung from roof and a weight is attached to it, the length will slowly increase with time. So it is my opinion that it is better to remove the weight after it is weighed.

In electronic weigh scales I have seen this effect over say 6 months of constant weight. The change is more than about 3% of full scale (in my case FS was 50kg)

No. It just keeps the next person from seeing what you weighed. Also, these scales, even the fancy ones in the club can get bumped and need to be re zeroed before you use to make sure you are weighing yourself starting at zero and not at 5 or minus 5.

I seriously doubt that it matters but maybe someone who is subconscious about their weight might not want anyone to know what they weigh.

Since the first thing many people do before stepping on the scale is check that it balances at zero. It is just polite to leave it that way when you finish using it.