Well I've talked about this before - but here are somethings about the bugged minibike - albeit I thought that they've fixed most of it.
Mods may cause you to have issues with the minibike - Just saying!
Lag on the server or client side can cause many of these 'bugs.'
Sudden disappearance: Generally the minibike will be there - just not where you expect it to be. It will either be:
1.) A head of where you were at IE: In the path you would have taken - so it's important to remember where "you were" - either visually or on the map. Sometimes your client can crash with a minibike issue and then when you return - it 'won't be there' where you expect it to be.
2.) "Behind you" or where you are at... So if you've remembered or are where you were when it disappeared - you can also look in the path you took to get where you are. Sometimes you'll find it 'behind you.'
3.) Sometimes it's gone underground because you're mis-treating it!

Usually when this happens you can hear a 'groaning sound' that as a regular in interval, sometimes you can actually see smoke and/or fire rising from the ground. Generally I found that they are not below 2 blocks underground. So - digging down 3 blocks means it won't be there - try another block, but I could be wrong. You will have to dig out 2 blocks and don't forget to dig out a 'ramp' to get it out; albeit sometimes just digging down to the right block actually can let it 'rise to the surface' for you.
4.) If you're at a 'base' with underground tunnels/structures it maybe down below. We had one in Valmod that went down some 12 blocks to 'live' in a hallway! It regularly went down there! But that was Valmod.
5.) You're minibike just took a nose drive into the ground either behind you or ahead of you; its just a combination of issues.
I think someone said that the issues with the minibike were do to its rate of speed, and numbers 1, 2, 3 & 5 show that it is a probability. In most of the instances there was either smoke or fire coming from the engine - not from the riders POV, but 'others' POV! IE: Others could see smoke, fire or an irregular sound coming from the minibike that was having a problem. From the user/riders point of view - everything looked normal. So... If a 'team mate' says your minibike is on fire - expect problems with it. Generally logging out and back in resolves the issue with not being able to ride/interact with it. But - if you've lost it you'll have to find it, but it's always a good idea to log out and back in.
With other issues such as 'falling through the world' - I don't doubt that a minibike and rider could experience that. Albeit 'we' haven't yet. One of the 'common' things that happen when a minibike is malfunctioning, or actually either the data associated with it on the client or server side is that the player at some point can not interact with it.
So... Do you have a mod installed?