I'm going to answer this question seriously...
This isn't rocket science, but something about the game is different than the practice.
Suspect it is the pressure, intentional or unintentional, about the "game" being applied by you (as coach), the kid's parents, and/or the game environment (screaming/cheering/yelling parents on sideline). Probably the game doesn't seem fun to them. Or it seems scary for previous reasons. One thing that really helped me understand how a game sounds to a kid was to video some games and go back and listen to it. At the time I started doing this, I was coaching. It was horrifying! I couldn't control parents, but I cut the amount I said by 90%. Also, kids are masters at perceiving stress in others-- again, if pressure or game environment is stressful, this can make a 3 year old completely shut down. Some of this you can control, some you can't.
It could also be that 5 year olds are really a lot bigger, faster, and stronger than 3 year olds. Strange kids (on other team) are scarier than known kids (kids on her team).
All that being said, best thing to do is try to look at these components objectively. You may not be able to "fix" this right now. This is a three year old we're talking about here. They can't wrap their head around all this. Organized games are meaningless to the development of this age group (aside from destroying their desire to play soccer, perhaps). A kid doesn't really even begin to understand their role on a team developmentally until they are 7/8 years old (and in some cases, older than that).
Personally, I wouldn't apply pressure to play in the game. I would let the kid decide whether to play or not. If she doesn't want to play in games, no worries. Have her practice. Make it fun-- this is the reason she plays, right? I would encourage the kid/parents to back out of games (maybe complete this season and find another venue for playing). If the kid really likes soccer, take a break on playing formal games for a year. Do skills clinics or something. Go to the park and kick the ball around. But back out of the organized games. The kid just maybe isn't ready for it. And (in my humble opinion) formal team games are 100% meaningless at this age to learning the game.