Look at this:
void loop() {
// put your main code here, to run repeatedly:
address=0;
// sizeaddr=sizeof(count1);
EEPROM.put(address, count1);
//count1 = EEPROM.read(address);
// address = address + sizeaddr;
EEPROM.put(address+sizeof(count1), count2);
//count2 = EEPROM.read(address);
What do you think, how many times the loop() runs in 1 second? This will destroy the cells in the EEPROM in a moment.
Fortunately put() method uses low level update function which writes only changes.