it could be a basic question for you guys, but i'm new in this.
is it necessary to stay connected to internet while doing solo-mining ?
is there any method to keep mining without permanent internet connection (i mean offline mining)?
You need to be online because mining is sort of like a mathematical race: whoever finds the hash of the next block (with value less than the current target) wins. And in order to prove that you found this value before anybody else, you need to be online in order to broadcast it to other users.
In order to be able to calculate the nonce for the next block you need all the information from the last known block. The time between the blocks is 10 minutes in average, so if you stay offline for more that 10 minutes you will not be able to perform any valid calculations and essentially you will be in a solo, forking mode, solving the wrong block.