No, there's not a problem. I had the same thing happen to me and emailed Leigh to ask what was happening. It seems that when you "send" a PM, it stays in your Outbox until it is collected by the recipient. It's not like email which just goes and you don't know if its arrived. If someone's away it could be there for days/weeks, but at least you know when it's been collected.
When it goes from your Outbox, it'll appear in your Sent file.