Kingpin;162185
I believe Fritz hypothesized that they left out Dana to play up Venkman's womanising in the show, a single Venkman chatting up every attractive woman he sees has more comedic value then Venkman and Dana's weekly interactions.

Short of some sort of official statement from JMS, Gross, or Medjuck, that's only a guess, but a solid one. Some other possibilities:

1. Dana wasn't a Ghostbuster, or an employee of the Ghostbusters. Zombie mentioned Louis–note that he didn't appear in the cartoon until after GB2, when he was hired as a GBNY employee. Dana never joined the company, and it wouldn't really have fit the character as portrayed to do so.

2. It was a show for Saturday Morning TV, and most eight year old boys think romance is icky. They might have thought that having Dana around would have made things too mushy. (Egon and Janine made it in because Egon starts off clueless, and the humor of her hamhanded flirtations could be played up–the actual development was very slow and subtle.)

3. Since Dana isn't a Ghostbuster, how many kinds of plots could she factor into, anyway? Either cameos just to show she and Venkman are still dating, or episodes where she's in danger again. They might have decided that, once again, she was too limited a character in the context of a “children's” action/comedy show to even bother with having at all. (Heck, they basically gave up on Louis pretty quick too)

I still have mixed feelings about the matter, myself. Her not being in the show before GB2 does make it “fit” the sequel a little better; just like Venkman and the others, we hadn't seen her in five years either. I still kind of think they should have gone ahead with the cameos and one or two “Dana in danger” episodes after GB2, though–Dave Coulier Venkman was mostly neutered anyway, and who knows? Having a steady girlfriend might have made him look less like a dumb creep.

ive always heard leagal/copyright/permission issues thats why nothing looks like any thing from the movie from the ghostbusters right down to the equipment. everything had to be redesigned but be instantly reconizeable

Unlike with XGB which is a story for another time, with the equipment appearance in RGB, I don't think legal/right issues was the reason for the redesign, but simplification for animation.

A simpler design is easier to animate, and bright colours make a given item more attractive to children.

The only significant issue relating to rights would involve the “likeness rights” of the principal actors… which the animators of RGB decided to not use, in favor of designs that resemble the principal cast, but with changes made to make them all unique from each other.

Seems logical

Several RGB viewers have pointed out that even thought Dana does not appear on the show,
both Anne Lawson from The Revenge of Murray the Mantis and Katrina from Russian About look some what like Dana.

The show (mostly) takes place between GB1 and GB2. In GB2, it's explained that she ran off to Europe. Most likely between GB1 and the Citizen Ghost episode (or the events described in Citizen Ghost). As for the episodes after GB2, we don't know what happened to Peter and Dana. Given their shaky past, she dumped him again. This is probably the case as she is nowhere to be seen and is barely mentioned in the Ghostbusters game, 1 year and 11 months after GB2. Apparently, Peter has been dating other women for quite some time before the game as they mention blind dates that he went on.

TheStrikeTeam21;162827
The show (mostly) takes place between GB1 and GB2. In GB2, it's explained that she ran off to Europe.

She married the Stiff, and he ran off to Europe, not her.

Well, there you go. But in any case, she wasn't with Peter. She was dating the stiff, so she wasn't included in his life.