OK, I'll bite, what happend when you tried running the same command with the ESSID included?
What card are you using? ath0 is what I see on my atheros card and if that's what you're running then I'm not sure if it's wrong, but I use ath0 for a managed wireless connection _and_ a monitor mode vap (tho not at the same time.)
airmon-ng stop ath0
airmon-ng start wifi0 # which sets up vap bringing ath0 back up in monitor mode.
Then I use the command you listed above but with ath0 as the interface.
I'm assuming now that your -a is the AP mac address and the -c is the mac of a wireless client associated with said AP.
Connecting to the AP in this scenario shouldn't enter into it. What this deauth attack does is send a packet to the client prentending to be (spoofing the source address of) this client's access point. You're not talking to the access point at all. I'm 99% sure there's no waiting for a beacon frame on a deauth attack but I can't test it this second.