If the laser leaves the centre of the centre-spot, there's a few reasons for this.
1,
The laser is not collimated. The piece I wrote discusses how to rectify this.
2,
Play in the drawtube of the focuser. Any play while you make adjustments to the laser/Cheshire will have the collimation/laser beam wonder off away. Some focusers can control the amount of play through a locking screw or a tension control screw. Other focusers need to have shims attached to the draw tube to reduce or eliminate play. This play will change the position of the laser/Cheshire/eyepiece/camera every time you make adjustments to the focus or tweak the piece in the focuser.
3,
Poorly fitting laser/collimator. Sadly these tools can be poorly made so that there is too much play between the tool and the focuser fitting. One solution is to wrap some tape around the fitting surface of the laser/Cheshire barrel to tighten the fit. Care needs to be taken here not to make the fit too tight and not to over tighten the set screws that secure the piece in the focuser so not to damage the tape.
4,
Crappy set screw design of the focuser! This is a real hidden trap. If the focuser has two or more set screws to hold the eyepiece in place, then this is a MAJOR problem for any collimation attempts!!! If you release and tighten two or more set screws, YOU WILL NEVER RECENTRE THE LASER, CHESHIRE, EYEPIECE OR CAMERA to the exact same spot EVER! This will always put the laser/cheshire/eyepiece/camera in a new position every time you make a change. The focuser below is an example of a crappy focuser set screw design with two set screws. And it doesn't matter if your focuser has the set screws push directly onto the piece or uses a brass compression ring, two or more screws are always bad news. You need to only use ONE set screw at all times, otherwise you will forever be fighting collimation issues visually and photographically, and in the collimation process.
5,
Primary mirror shifting in its cell. This you will really only see when the scope is altered in position from vertical to horizontal, and even rotation. This means that there are issues with the mirror cell: springs are too weak (VERY common problem and mass production scopes all have undersized springs - just to save a few cents), too much play in the cell mechanism, mirror is loose in cell, locking screws not fixed (careful when fixing the locking screws as these WILL ALTER THE COLLIMATION! You need to fix the locking screws with the laser on to see that collimation is not altered), cell is loose in the OTA, cell/OTA is poorly designed/fabricated.
6,
Secondary mirror shifting. Like with the primary mirror, this is only noticed when the OTA is moved about.
These are the only ways in which I can determine as to why a laser beam/collimation will actively shift.
If the secondary mirror is not properly set, ie: not square with the focuser, but held securely in the holder, the laser will not go for a wonder. It can't if everything else is fixed. But it will mean that the scope is not properly collimated.
A focuser that is not square also won't see the laser beam wonder off, but it will affect the collimation because it is not properly set in the optical train. Can be tricky to verify if your focuser is not square, though it is not difficult to rectify, but it won't alter the position of the laser beam or collimation if it is not square.
If you see the laser beam go for a wonder, you need to go step by step, one at a time to eliminate any of the variables. And different scopes will have different idiosyncrasies.
Alex.