Well, I can see it going either way.
Let's say you have two opponents: a pirate and an angry marine. It's some kind of bar fight, obviously.
The initiative order is marine, you, pirate.
Round 1:
Marine attacks you with his fists (Melee/unarmed). You parry. You're at -1 DM until ... some time. Doesn't matter yet.
You go kung fu all over the marine's face (Melee/unarmed). The marine parries.
The pirate attacks you with a cutlass (Melee/blade). Wow, dude, way to escalate a simple bar fight. You parry. You're -2 DM now...
Round 2:
Now, if parry/dodge penalties reset at the top of the round, your -2 DM goes way. I'm guessing this is not the intent of the rules, but stranger things have happened.
The Marine grapples you. Opposed check. If you still have that -2 DM, it matters a lot. If it reset at the top of the round, you're free and clear and grapple normally.