is the KOH going to absorb the C02 forever?

Yes, KOH always absorbs CO2 availabe to them. 
It reacts with the CO2 to produce Pottasium carbonate and water.​

CO2 + 2KOH K2CO3 + H2O
 

 

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No
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why?
 
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yes but only till the co2 is,present after the absorption of entire co2 from a place it will not be able to absorb it

hope this will help u
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