I don't believe there's anything to worry about. Your MBP will automatically shut down if it's reached the end of its reserve energy. Your best advice is to make sure your battery is at 100%, then start using your MBP. Everything should be fine. I don't think you'll need to visit your Apple Store - yet, anyway.
Leave a message so we know how things turned out!
Depending on the model … by following for a while Apple's routine for care and maintenance of the battery for that particular model, you might be pleasantly surprised by the ability of the things to resume normal behaviour at 'low points'.
If the next trip to deep sleep (or whatever it's called these days) fails, the one afterwards might succeed. And so on. Whether the logic to get things honed is solely within the battery, or outside the battery, or both I don't know for sure but I have had extremely good results with my own battery (MacBookPro5,2) despite often not caring for it as i should. Suspect that Apple really did their homework with this class of laptop. Hopefully similar for yours.
Hope that helps
Open up a Terminal window & copy / paste the following command:
pmset -g pslog
That will start a log file specifically for what is happening during sleep / shutdown that the Apple Store tech will be most interetsted in & will very much help if there is something going wrong, to hopefully identify the cause.
Also, if you hold Option and click on your battery icon, does it say the health is Normal?
Below: a screenshot of coconutBattery taken before joining this topic.
The shot links to a folder with a text file showing my ioreg result.
On a few occasions whilst using Snow Leopard — on the first occasion, for a few days — the system advised:
Service Battery! (as pictured by TUAW in 2009)
— and I vaguely recall seeing the same, or similar, once whilst testing Lion.
When the exclamation was first given, I began following Apple's advice. Kicked myself relatively hard for never bothering to remove the MagSafe. After a few days, I can't recall how many, I arranged an on-site visit from an authorised service provider. By the time the visit was made, the specialist test revealed no problem and indeed — by that time — the system had ceased to offer the alert.
After each such incident I drift back into very bad habits (MagSafe rarely removed).
Then when I see the alert: I kick myself just lightly, begin to do the right thing (remove the MagSafe appropriately) until the caboodle reaches a point where the battery can properly allow deep sleep.
I no longer bother to seek the service suggested by the system. It seems that the computer itself performs the service — if I treat it nicely.
I recently bookmarked the following page: 15" PowerBook Battery Life Tests (George Schreyer, updated 2010) — not the most recent, but a suitably detailed starting point if ever I need to dig deeper.