Does armor dex mod apply to your knockdown check?

No.

In fact this is one area where I think armour should *positively* modify your DEX against being knocked down.

I believe it would apply to those who are untrained in wearing armor.

Really? Do you have a page number for that? I'd think it would-- with the armor bonus, someone with chainmail (11) has only a slightly better chance of staying on his feet, as opposed to being impossible to knock over.

Knockdown is figured regardless of armour, so a person wearing chainmail (or any other armour for that matter) is no harder to knockdown than someone who isn't.

Since knockdown is figured against SIZ, and therefore affected by weight and mass, I have thought about giving a bonus to resisting knockdown depending on the armour worn as the defenders weight and mass is obviously increased... but why bother. It works well enough and keeps people on their toes, or their backs ;)

p. 79 of the rulebook:

Encumbrance is not used to modify a DEX roll for bal-
ance unless the Gamemaster decides that it should, based
on the circumstances. However, difficult footing may im-
pose a negative modifier as usual.

As for armor reducing the chances of a knockdown:

Whenever a character takes a blow, whether from a
weapon in combat or some other source (such as riding into
a tree limb), the base damage ? i.e., the damage dealt be-
fore the victim?s armor, if any, reduces it ? is compared to
his SIZ value.