I have been running multi-player games for my club for three years, first using BLB and now BLB2.
I am not certain as to what you mean by fragility of the support rule. I am guessing you are referring to the bonus that support adds for morale tests.
I do not find it to be an issue, especially when "fighting" my army using period tactics. Having both flanks and rear "open" and unguarded should have a detrimental affect, imo.
As you may have found, ISOLATED units have a tough time sticking it out, but I really do not see that as being outside the bounds of reality.
One thing, many new players to BLB2 (from my personal experience of running games) want to test morale in situations where such tests are not called for. For example, taking one shooting casualty and then testing for that.
By following the conditions for morale tests, on the charts, there is no confusion.
This may or may not apply to you, but there you go.
As far as changes/house rules:
1) In order to speed things up for larger multi-player games (6-10+), I changed the close combat from a continual multiple round fight until resolved in one turn to a one of 3 rounds of close combat per turn, then advance to the next phase. This helps keep things from getting bogged down for other players.
In a 1v1 or 2v2 game, I leave it as written in the rules.
2) In larger games, I allow the morale bonuses of "The Commander is with unit/gun" and "The Commander is within 12" and in LOS" to apply for commanders of the wings as well as the CinC.
Again, in the usual games of one or two opponents, I leave it as written.
# I have been working on, from time to time, a fast play version of the rules for my club, as I still get comments from newer players that the game "is too slow." I do not hold that opinion, myself, nor do my regular group of players who is far more familiar with the rules. However, being a club event, I want everyone to push troops and roll dice.
# Another thing to note about morale tests. If you have a disordered unit that is forced to take a morale test, and you end up with a modified result of 4+, the unit recovers from its disorder, in addition to passing the test for the circumstance causing it.
# The author of the rules as publicly stated that players can feel free to make any changes they wish to make the game the "game they want to play." So, if you want to tweak, tweak away.