if a tenant defaults on rent a section 21 is issued giving 2 months notice to quit the property. if the tenant 'makes good' and then stays, does the tenancy carry on as normal once the tenant has made good or can they still leave during that 2 month period from immediate effect?
That would be up to the Landlord or agent whoever issued the possession notice, if the tenant has not paid once they may not pay again. I would let the section 21 notice stand, do make sure the possession notice it is valid.
"or can they still leave during that 2 month period from immediate effect?"
Are you asking whether the tenant can leave during the 2 month notice period, having paid off the rent arrears? If so, I'm not sure but I suspect not. I think the tenant would (assuming it is a periodic tenancy & not a fixed term one) have to give one month's notice to expire on a rent day.
My letting agent issued a section 21 to my tenant when he paid late, again. The tenant was given 2 options, either find a guarantor or pay an extra month's rent this month so he's paying in advance. He agreed to the latter. If he does pay the 2 months, the letting agent will rescind the section 21. Meantime, he can give 1 month's notice if he wishes.