This has happened so many time - Grrrrr is right! This last time I sent evites from Pingg and if I don't get the yes or no replies I can "nag" them with a "reminder" note. :) It's has worked great so far.
The first school party we did, not one person RSVPed. It was 5K so no parents knew each other - but still.... my phone number and email was on the invite. How hard is that? I ended up verbally asking moms outside of the school at drop off and got a few to come.
His 2nd had some RSVP's and then a bunch who showed up without RSVPing AND they brought their siblings. I had to pay 10 bucks per head over the limit. I finally had to start mentioning that yes they could stay but you have to pay the 10 bucks at the counter. I then of course was short on pizza and cake. Soooooo Annoying!!! Plus they brought one small gift for their invited kid and stowaway. Which I would usually never care about, just added fuel to the fire.
Anyhoo, I feel your pain. Next time go the route of the evite. My DH thought it was weird but in this kind of situation it's brilliant. Just don't use it for a wedding invite LOL