I think I follow you. You seem to be using the add-and-wait method. Add ammonia solution once it fells below 2ppm, so your bacteria don't starve. Also this seems to be a cold water tank. Are you cycling without a heater? If so, your fishless cycle should last longer in comparison with warmer tanks.
Do you have nitrates readings in your tap water?
It seems that you may have overdosed your tank somewhere down the line, which -some have reported- stalls the cycle for a while. Of course I'm just guessing here.
If I were you, I would do a 50%
water change (or more if needed, read along) and go for a modified version of the "add daily" method:
After 50% WC, wait for 20 minutes and measure for Ammonia. If it's below 2ppm, try to raise it to 3ppm but avoid crossing the 6ppm upper limit (it's OK if you increase to 4 or even 5pm). If it's above 3ppm change a bit more water until you get close to that target and adjust if needed be.
Wait 12 hours and measure again. This way you would gauge if Ammonia is being processed.
Once you confirm this (say Ammonia is at or below 2ppm and it was at say 3 or 4ppm 12 hours ago) measure for nitrites. You'll know you have a nitrite spike when the reagents turn red without waiting time for the color to show. In a cold tank, the nitrite spike might take some time.
At that point be careful not to overdose Ammonia as you keep feeding your tank. Just keep adding Ammonia to brake the 2ppm "floor" without braking the 5ppm ceiling (in measures made 20 minutes -or a bit more- after adding it to your tank). In short time, you are going to get readings of Ammonia of zero in 12 hours (once your tank is fully cycled readings will be constantly at zero). When you observe this is happening, wait for nitrites to fade down. The nitrite spike usually takes a bit more time than the ammonia spike, nitrates we take care with water changes.
One more thing, false positives in Ammonia are likely to happen if your water is treated by the City with chloramines if you measure right after adding the water conditioner with a Nessler reagent test (such as API Ammonia test and most others).
Pepe
Santo Domingo