Test your tap water first, make sure that's not the source of the problem.
If not, there 2 issues here - The water changes you are performing are removing the ammonia and nitrites that your nitrifying bacteria needs to feed and establish itself, so in otherwords you are slowing down the process by doing so..
Also if you can't get your Nitrite/Nitrate to stabilize, its a sign that you don't have enough biological media (surface area) for all your nitrifying bacteria to establish.. Add some biomedia (biomax beads, matrix, sponge filter, etc) and be patient - maybe use a bacterial supplement like Seachem's Stability.
Time will stabilize the tank, but not if your slowing it down with water changes or lacking surface area.