Which is the correct possessive pronoun in this example? our vs their

Which is the correct possessive pronoun in this example?

1. "Those of us who wear glasses should have our eyes examined at regular intervals".
2. "Those of us who wear glasses should have their eyes examined at regular intervals".

Solution 1:

In the most likely reading of these sentences, the speaker is among those who wear glasses. In that case, it is the first one:

[1] Those of us who wear glasses should have our eyes examined at regular intervals.

Compare to the following examples from published literature:

Those of us who are part of this journey know that our lives do not obey a certain order and that events do not occur in a predictable manner. (source)
I pray for those of us who know that honor of giving of ourselves to protect... (source)
The problem was that to those of us who were weak or fat, there was, in our eyes, no hope that we would ever be able... (source)

Test preparatory materials make the same point.

Pass Key to the TOEFL: Test of English as a Foreign Language (p. 187):

Incorrect:   Those of us who are over fifty years old should get their blood pressure
                     checked regularly.
Correct:      Those of us who are over fifty years old should get our blood pressure
                     checked regularly.

Barron's GMAT: Graduate Management Admission Test (p. 144):

Incorrect:   Those of us who care should write to their congressman.
Correct:      Those of us who care should write to our congressman.

When their would fit

There are at least two kinds of contexts in which their would be appropriate†. They are quite rare, and I haven't been able to find examples of them in published literature. Nevertheless, here they are.

First, imagine the speaker is addressing his fairly large family. Imagine also that although some members of the family wear glasses, not all of them do, and, in particular, the speaker does not. In that case, it would be appropriate for the speaker to say

[2] Those of us who wear glasses should have their eyes examined at regular intervals.

Second, there is an even less likely context where their would be appropriate. Imagine the speaker is a parent addressing a group of parents, some of whom wear glasses. In this case it doesn't matter if the speaker wears glasses as well. The speaker is discussing arranging eye exams for the children, in particular who should be making the arrangements. For whatever reason, the speaker thinks it is the parents who wear glasses who should be making the arrangements. Now when he utters [2], their refers to the children. The speaker means the following: 'Those of us who do wear glasses should make arrangements for the kids to have their eyes examined at regular intervals.'

^{†Thanks to Edwin Ashworth for pointing out that there are such contexts.}