Recent versions of PuTTY automatically initiate repeat key exchange once per hour, to improve session security. If your client or server machine is slow, you may experience this as a delay of anything up to thirty seconds or so.
These delays are inconvenient, but they are there for your protection. If they really cause you a problem, you can choose to turn off periodic rekeying using the ‘Kex’ configuration panel (see section 4.19), but be aware that you will be sacrificing security for this. (Falling back to SSH-1 would also remove the delays, but would lose a lot more security still. We do not recommend it.)