This is a position similar to a ten thousand year ko. White takes the ko, but after Black passes White should not fill.
passes and fills. almost fills with the bulky five shape. White is not obliged to capture however, so passes and captures.
The gun six is not ideal and White can at least make seki.
White almost fills with the bulky five. passes and eventually captures. This time, the eye shape is sufficient to life unconditionally.
Therefore, neither side should fill the ko because they end up worse off than just leaving it open. They would both like to capture the single stone in the ko, however, and this could create endless repetition. Spight rules end the game after White takes the ko for the second time, because Black passes for a second time in the same position. The game stops "unnaturally" favouring Black.
Bill: Very interesting position. :) BTW, at the end I think you mean, favouring White. If indeed, neither player wants to fill the ko -- and I think that is so --, then this challenges all rule sets except forms of no pass go. For instance, under no pass go with prisoner return Black has no prisoner, and so may as well resign after White takes the ko.
To conclude, it is undesirable for either side to fill the ko under area scoring. If Black fills the ko, Black would lose 6 points (from B+2 to W+4). If White fills the ko, White would lose 2 points (from W+2 to draw). It can be critical, e.g. if komi is -1 point. Under Kee Rules, White would win if neither Black or White is willing to fill the ko. It is justified because White captures first (see 2x1 board in Kee Rules).