You might want to start over and re-evaluate your initial component placement by seeing how the rats nest of unrouted connections gets simpler or more complicated with where you place the components. Component placement can make all the difference in how a board can be routed.
Next my recommendation, from years and years of experience, is to ditch the auto router concept and to hand route the board. Humans are much better at visualizing things in multiple dimensions than a dumb computer program.
If you insist on the use of the auto router then just set it up and let it run till it reaches what ever percentage that it can achieve. Give up trying to shoot for 100%. Take the result you get and you can see the remaining connections that need to be routed via the still straggling rats nest connections. Use hand routing techniques to get these final nets in place. If you are using only two layers for connections then sometimes there may need to be a jumper or two to achieve 100% as the auto routing may have packed some things pretty tight in some areas. If you are using four connection layers it has been my experience that you can get it routed.
One thing to seriously evaluate is the design rules that you are using. Clearly routing with 6 mil lines and spaces is easier to complete a design than one where 10 mil lines and spaces are used. Of course finer geometry routing may require using a PCB fab house to make your boards if you had grandiose ideas about etching your own boards. (BTW I always use a fab shop to make my raw PCBs because of the quality that can be achieved over the low quality that is typical for hobby etching).
