Finding maxis with sleeves is really tough. I once asked a retail employee if they had any maxi dresses with sleeves in stock. He looked at me for a minute and said, "they make those?" Yes, sir. Sometimes they do.
Whimsical Garden Maxi Dress - Forever 21 - $24.80
I tracked this dress down after spotting this very pretty picture on pinterest. I just love the feminine boho vibe.
Here are a few other pretty maxi dresses with sleeves (under $30!):
A Wear Jersey T-Shirt Maxi Dress (more than half off!)
Cross-Front Jersey Maxi Dress (nursing friendly)