It depends on the shoe, but I have sometimes cut out a piece of suede to patch over the eylet and it works great. I'd make the patch in the shape of a "D" and glue on using textile glue with the curved part downwards, keeping the straight line on top unglued so that the lace can still move freely through the hole. It's a bit involved, but worth it if you plan on making the pair last a while.
Additionally, you can shoe-goo over the patch when it starts to wear down.