You can vote more than once, until it stops displaying his rank. Then you have to change computers or ip addresses (if you can or know how to do that).
The online results don't affect the print results really but last year I had a shitload of fun voting the HSM cast up the chart (I think my main goal was to keep them higher than Michael Cera and whatsherface from Juno).
It was funny cause when it started you could vote about 50 times per ip address. Then they realized everyone was just voting a lot and they kept lowering the limit, eventually ending up at about 15 per ip. So vote early and vote often.
ETA: It seems different this year. Last year it seemed based solely on number of votes, this year it seems based on refresh rates. If you refresh slowly (instead of my automatic reload of like 3 seconds, lol) it seems like you can vote indefinitely.
Also I should clarify: yes, voting doesn't influence the official Time Magazine results they print, but it does determine the online "Your Time 100" list.
So keep voting, lol. We can get him in the top 100 at least.