I often use the skype app for messaging, but every now and then I do not receive a message. I have windows skype running at the same time, and use android skype when I walk away from the computer. Sometimes a conversation doesn't make sense to me anymore.. and when I go check my computer it appears there's an extra message i didn't get on my phone. I haven't yet established if this is caused by being signed in on both pc and phone. As far as I remember, i haven't missed any messages when it was just on my phone, but I only ever find out when I go back to my pc.
On a side note, the app works great, and it's almost always on. Great call quality both video and audio, good and easy interface, i love it.
I just don't get all of the messages people write to me. They are left out in the middle of the conversation. Skype is always synched. And if I manually sync it now, it's not bringing up that message that I do have on windows. Somehow it just doesn't show some messages..