Support gets but, even if the unit doesn't get dislodged. All support holds prevent is dislodgment.

grrrr Support gets CUT. So Rum's support on the move was cut by the attack. You should have had Bla support the move and it would have gotten in.

In the last phase, I had it supported by two, yet it still was cut off because of the move and support of one??

That's right Attavior, yes. Any attack whatsoever ALWAYS cuts support.

"I had it supported by two" - your support prevented the unit from being forced to retreat, but it still loses it's ability to give support.

Any attack, whether it succeeds or fails, always forces the attacked unit to 'hold', meaning the attacked unit cannot give support to another unit - irrespective of how weak or strong the attack is.

This is a very basic rule of the game. It is made clear in the "introduction to diplomacy" in the help section of this site.

There is no error or bug.

Think is real life terms. Your a general and you have been ordered to support another general's forces into somewhere, but the enemy attacks you from another location. It doesn't matter how many other armies are supporting you as well, you have to hold your line so you can't help the other general.

ANY attack on a unit will cut it's support unless the unit attacking is the one against which you are supporting an attack.

A attacks B, C supports A attacking B, B attacks C, then support is not cut.

A attacks B, C supports A attacking B, D attacks C, then support is cut no matter HOW many units are support holding C.

Final possibility is -

A attacks B, C supports A attacking B, B attacks C, D supports B attacking C. Support is cut, B moves to C, but A still moves to B because B vacated when it moved to C.

There needs to be in a disclaimer in the help section that it is just superficial introduction to how to play the game. Players need to read the official rules from cover to cover.
http://www.wizards.com/avalonhill/rules/diplomacy.pdf