Do you handle the voltage translation correctly between the SIM800L and arduino UNO?
The SIM800L has 2.8V logic, where the Arduino UNO has 5V logic. If the Arduino is putting 5V into the SIM800L RX, TX, or RESET lines you are likely to get undefined behavior and possibly damage the SIM800L. Also since the SIM800L is only outputing max 2.8V (probably more like 2.5-2.7V) for logic high, the Arduino UNO likely doesnt see this as a high enough voltage to trigger logic high.
You will likely need a level shifter to do this correctly (I think sparkfun has some, something like: https://www.sparkfun.com/products/12009)