I've been doing this pretty much the whole season now. My longest streak so far is 11 games and that just ended over the weekend so I started a new streak today. There is also a home run beat the streak which I've made picks for maybe 10 times this year when I remember and have only correctly picked a player to homer once.
I'm at 16 currently. My one miss included a line out, a BB, and a (Grrrrr) IBB on the last at bat. I did luck out the other day on a game that my selection didn't put up a hit until the 11th inning.
I've been doing it for a few years now. My longest streak was 31...which also happened to be the first 31 days I played. I haven't been above 15 since then.