Can we know the limit of the number of times information can be stored/retrieved in computer chips - hard disks and RAM?
You want to be more specific about which memory:


For regular RAM there is no practical limit on number of times you can store the data. The chips will wear out, but this is mostly affected by power supply voltage, ambient temperature, background radiation and other things.
FLASH chips (for example, the ones in solid state disks) do wear out. There is a lot of articles around it -- google for "flash endurance" or "SSD endurance". The individual flash chips can be overridden between 1000 and 100_000 times, depending on technology. Commercial SSDs have 'spare' flash cells and complex algorithms to use spare cells instead of the ones which failed. 
'harddisk' are not semiconductors, but they still wear out because they have mechanical parts -- motor, moving arm, etc..


If you care about devices used in the computer, you may want to ask the questions in the other stackexchange sites. For example: 


https://superuser.com/questions/873590/how-many-times-can-i-format-a-hard-disk