Yes, p2pool is different than normal PPS (pay per share) pools. When averaged over a few weeks, you will receive a higher payout with p2pool than any other pool (assuming average efficiency). However, on a given day you will see lots of variance and shares expiring. That is the pool operating normally.

It will be frustrating the days you have bad variance. The new version of p2pool increases the lifetime of shares and makes it easier for ASICs to mine, so hopefully hashrate will increase and variance will decrease.

Actually, "normal" PPLNS pools such as BTC-Guild behave the same way as the frustrating experience you mentioned, it's just that their hashrate is so much larger you don't notice. This is what they are currently posting:
Average luck this difficulty is 106.65%. The following is the average luck per 10 shifts this difficulty:

112.47%  90.83%  104.68%  110.03%  110.16%  97.19%  122.84%

so BTC-Guild has some time periods where people are getting paid 10% less, and some where people are getting paid 22% more. Overall the variance is lower since they have more hashing power.