LTC4054 Odd behaviour
While it is entirely possible you have a damaged or counterfeit IC, the first step is to measure the charge current near the end of a charge cycle.

The LTC4054 mirrors the battery charge current by 1/1000 out the PROG pin of the IC (plus 3 uA): 
 

During the constant-voltage charge phase of the LTC4052, measure the voltage across resistors \$R_{PROG}\$. In order for the LTC4054 to observe an end of charge condition the voltage across \$R_{PROG}\$ should drop below 100 mV.