You're probably stuck getting whichever Eeveelution the time is frozen at, meaning if the clock in your room (the only way you can tell what time it is in the game, oddly) is stuck on an AM time, you're only getting Umbreon and if it's stuck on PM, only Espeon (I know it seems backwards, but they basically used noon and midnight for determining their evolution).
......Wasn't there an issue for something like this a long time ago, though? (the Berry glitch fix or something...)