Router bit keeps coming loose and cuts deeper into the timber

I feel your pain! This is not uncommon. If the bit is slipping out of the collet, it is probably due to a dull bit. The 1/4 inch shanks are more prone to this than the 1/2 inch ones, which is why most new routers use 1/2 inch. (Think about the large size as being analogous to a larger wrench being able to exert a greater torque.) However, if the problem is the housing slipping on the base, you can try wedging a little piece of sandpaper under clamp. If the clamp has a thumbscrew, use a wrench on it to tighten it just a bit more than you could possibly do it with strong fingers. It was just this problem that inspired me to ditch my old Craftsman for a Porter Cable. Good luck!

Several possibilities--- Are you using a short and stout extension cord plugged into a robust outlet? Is the bit dull? Are you taking too heavy of a cut? If you are cutting a wide or deep slot you should probably take it in 2 or 3 passes making the slot deeper each time.Good luck.

Have you tried taking out the collet and cleaning it and the cavity where it goes? If there is any wood dust present it may be causing the problem. If that doesn't fix it, you may need a new collet.

I've had this problem with off shore bits, where the machineing on the shaft is slightly under spec. The bit wobbles out of the chuck because it can't be tightened enough. Try a different bit.

The chain adjuster does not actually hold the guide bar, that is done by the bar nut/nuts, the main reason for chains coming lose is inadiquate chain oil to the bar/chain, does the chain look dry? it can also be the result of what you are cutting, if it is very dirty timber or railway sleepers.

Use a guide to your router from "riding up the board".

Well I'd use a 3" Forstner bit to cut the hole, not a router. Here's a link so you know what I'm talking about: http://www.amazon.com/Steelex-D1024-3-Forstner-Bit/dp/B0000DD0KZ
A forstner bit is more precise but usually not used in a handheld drill situation. A keyhole saw may be too imprecise for the rudder although a dedicated (not interchangeable) keyhole saw is one option. The depth of the cut would be the other problem here.
A VERY slow drill setting is required. A high torque, low speed drill suitable for use with a diamond cutter hole saw would be best. i.e. max 450rpm.
In the boat building industry you would normally use a guide that you bolt to the rudder or mast to drill such a hole. I don't have a ready reference for such a guide but you may have luck simply asking a local boat-builder (very very nicely) to borrow one! It is easier to drill three mounting bolts into the rudder to hold the guide and later backfill with a quality (read "marine") epoxy.
A boatbuilder I worked with had one such mount specially made. It is simply a flange turned from steel - the harder (the steel) the better but also more expensive. Three bolt holes in the collar allow for mounting. The centre hole is the exact right dimension for either a drill bit or forstner bit.
The problem on the rudder is the non-flat surface. A piece of packing timber, crafted to match the curved surface to a flat plate is the best idea.
As an alternative a special drill-bit like a fish-tail can be used. These bits can be used at high speed to cut an accurate hole at the size you want. It all depends how exact you need to be.
Whatever you choose, trial the hole and hub cuts in a similar grade timber first. Whichever way you go the standard solution is a custom solution!
I would suggest a plug cutter for the hub and FAMAG is the best, made in Germany. A matched pair for 3" i/d and o/d is the best option for an exact match. This is the normal procedure for such a boatbuilding operation.
Good Luck!

could be a couple of things
1. too deep a cut could pull too hard on the bit and make it lower

2. bit not all the way in the chuck. put bit in as deep as possible, then pull out about 1/16 inch, then titen

hope this helps

That would be the only thing to cause this type of a problem. I had the same problem replaced the part and away I went like nothing ever happened

This may not be related to your jig. It may be movement in the vertical axis resulting from:

1. The router bearings being worn allowing the bit to move up and down.
2. The router bearings worn allowing the spindle to deflect side to side which changes the bit height slightly (cuts on the edges, making the cut a hair deeper).
3. The router collet or router spindle worn, allowing the bit to move during cuts.
4. The jig guide plate deflecting or no longer flat.
5. Excess vibration in the router causing the wood to move in the jig.

To check the bearings; try routing the cut with a straight bit first to clear the wood for the dovetail bit. Then cut with the dovetail bit (a new one preferably) using very light feed pressure. Is the joint tighter? If so then the bearings are worn. Have the router serviced or replace it.

Check the end-play by pulling on the router shaft, does it wiggle slightly in and out? If so this is your problem. Have the router serviced or replace it.

Be sure the wood is flat and the faces planed parallel, if they aren't the dovetail line will be straight but when you assemble there will be slight end gaps in sections of the dovetail.