There are ways to detect intrusions which have not been done with all possible stealthiness, e.g. noticing abnormal battery usage or weird modification dates on files. A competent intruder will avoid leaving such clues, so this is not a reliable detection method, but if you actually see something fishy on the machine, then chances are that something fishy happens.
You say that the machine was compromised one month ago. Did you reformat it and reinstall the OS from scratch ? If you did not, then chances are that the machine is still compromised. You cannot be sure that whoever installed a key logger, installed only a key logger. For that matter, nor can that person be sure of it either. Key loggers are software created by people with at least partially malicious intent, and there is no limit to malice; something advertised as a key logger could also plant extra backdoors of its own, unknown to both the target user (you) and the wannabe hacker (the one who installed the key logger).
Thus, no salvation except by nuking the complete machine.