CLS, you do pay 20cents ever time you renew... but if you don't have anything new to list, it's a great way to push yourself up the search.
I list/relist/renew when I think of it... which is usually at about this time of day! But I don't really have a strategy as such.
I too have found that mid-afternoon UK time gets far fewer views... whereas if I renew now, I get more fews in a few hours.
I presume it's when America is switching on it's machines and browsing- but before other sellers over there have listed anything.