The battle will lose its appeal for her after awhile - especially if she sees that she has missed out on things because the time out has gone on so long. Be honest with yourself, how many times have you ever seen a punishment of this sort through? Or do you try to distract her out of a tantrum, or jolly her out of it?
If she keeps running away you could put a toy into 'time out' until the next day for every time she leaves time out. The depletion of favourite toys will eventually register with her. Children aren't silly, they do understand consequences.
At the end of it all you say 'well that was silly, instead of a 4 minute time out, you lost 30 minutes - you could have watched 3 Octonauts shows in that time, 3 whole shows, gosh, that's a lot, isn't it? And poor bear and doll will have to sit in time out until tomorrow now, that's very sad for them. And that's not because you were naughty by doing X (whatever action caused her to get her initial punishment) but because you kept running away from time out. (DON'T take a special bedtime toy though, that would be too cruel.)
It may help to have a discussion about using time out as a punishment BEFORE any bad behaviour. Sit her down and have a 'chat' about what will happen if she's naughty or mean to her sister, and that the punishment will be 4 minutes in time out. Get her to repeat to you what the punishment will be. (1 minute for each year, and she's a big 4 year old now). Then when the time out happens she will KNOW what's going on, and it will make the post time out/tantrum discussion that little bit easier.
Funny incident was once when I was visiting my sister, I told DS1 off for something and he went and took himself off to time out without my sending him - my DSister just about wet herself laughing as quietly as possible. She said 'I gather time out has happened a few times before?!'. (I did call him back!)
And this is a boy who took a LONG time to get used to the idea. I'm not saying he's always easy to send to time out, but he knows that I mean it when I put him there. Every now and then we have a mammoth one, but then the next ones swing back to normal.