does BTC work on a half life or time lapse for me to just store a(n) receiving address ?
I don't really get your question... As long as you have the private key, you should be able to spend unspent outputs funding the address corresponding to the public key generated with this private key.
In layman's terms: as long as you keep your wallet safe, you can keep funding your address forever...
for ex: cold storage wallet receiving BTC will always be ready to receive BTC no matter how many time the address changes?
As long as the address is generated by the cold wallet, yes, it'll always be ready... You can even re-use the deposit address if you want, altough it might decrease your privacy if you do this...
