Why keep baptismal fonts full in the Roman Catholic Church? In our (Presbyterian) church, we have a stone baptismal font in which we fill with water whenever we need to baptize somebody. At other times, it's empty, more for reasons of plumbing than doctrine - apparently there's some chance it could be damaged if kept full, due to its age and design. Our minister mentioned that in the Catholic Church, this would be considered wrong, as the font is meant to be kept full at all times, with the water traditionally being replaced each year at Easter.

What is the reason for this custom of keeping the baptismal fonts full? Is it a strict requirement or just a common practice? And as a practical matter, how is the water kept clean if it has to last all year?
They're not kept full all year long,  there is a  blessing concerning Holy Water that takes place solely during the Triduum. But that is not the water kept in the font.

There is a fairly erroneous Catholic tradition that some priests take part in where they dump all the Holy Water before Lent starts then fill them back up when Easter comes around. 

What we do get fresh before Easter are the three Holy Oils and the Easter candle for the year. But a priest could bless water, salt or whatever whenever he wants to.  It could be said that Easter Blessed water is better, but it's probably just as good.

http://www.fisheaters.com/water.html