In addition to or instead of a neuro-ophthalmologist, you may also want to see a behavioral optometrist. They can and will test for convergence insufficiency and other problems caused by your eyes not working together properly.

You can get referrals at http://www.braininjuries.org or http://www.nora.cc

You may be able to hold your eyes correctly for some time, but the effort required to sustain it may be too much for you to do it all the time. Vision therapy could strengthen your eyes and eliminate or reduce the moments in which you slide out of focus.