Is there any reason a chicken's egg would lose color?
Yes, and it doesn't necessarily mean anything is wrong.
I don't know how long yours have been laying. The longer into the laying cycle the more the egg shade can lighten. A green egg may look almost blue. A brown egg can look almost white. The basic color won't change, like from blue to white, but I've had hens that normally lay a brown egg lay almost a white egg just before they molt. This is a slow gradual change, probably not what you are seeing. Sometimes it is so gradual you don't notice it until you do.
The egg stays in the shell gland for a long time with the hen adding a layer of shell material to the egg. This takes many hours. Then the last half hour or so the egg is in there is when the hen adds the brown coating. If something happens to cause the hen to lay the egg early the brown would not be applied. The egg would be white. If it is laid early enough it could be thin-shelled. What might cause her to lay the egg early? Some kind of disturbance, maybe a perceived predator threat or just flock excitement. Until your last post I thought this might be it but it would be unusual to get two eggs like this.
Both had thin shells and were definitely white. Could it be my older hen getting to the end of her egg laying?
How old and does she normally lay a brown egg? Older hens can develop egg laying issues. Not all do but it's not that unusual. Typically that would be at least 4 years and probably older. The number of eggs she lays also typically drops.
How long has it been since a molt? At the end of a hen's laying cycle (right before the molt) they can start laying strange eggs. This is different than the egg shells getting lighter. The egg quality can diminish. Their bodies wear out and they need to molt to refresh everything.
There are some diseases that can cause this. If the hens are acting normal and not acting sick and if it is only one hen laying weird eggs this is probably not the problem but I have to mention it. Pay attention to how they are acting and see if you start to get other weird eggs. Try to not get too excited about this unless you see other evidence. And see how consistent those white eggs are. If this goes away it is just a glitch.