Has a Pope ever encouraged separated or civilly-divorced spouses to strive toward reunion? Has a Pope ever encouraged, such as in an official letter or audience, separated spouses to strive toward reunion?
The Catechism of the Catholic Church (CCC), issued by Pope John Paul II, says that reunion is the ideal that should be sought, if that is possible:

Yet there are some situations in which living together becomes practically impossible for a variety of reasons. In such cases the Church permits the physical separation of the couple and their living apart. The spouses do not cease to be husband and wife before God and so are not free to contract a new union. In this difficult situation, the best solution would be, if possible, reconciliation. The Christian community is called to help these persons live out their situation in a Christian manner and in fidelity to their marriage bond which remains indissoluble (No. 1649).

Moreover the Code of Canon Law (CIC) says

Can.  1151 Spouses have the duty and right to preserve conjugal living unless a legitimate cause excuses them.

and

Can.  1153 §1. If either of the spouses causes grave mental or physical danger to the other spouse or to the offspring or otherwise renders common life too difficult, that spouse gives the other a legitimate cause for leaving, either by decree of the local ordinary or even on his or her own authority if there is danger in delay.
§2. In all cases, when the cause for the separation ceases, conjugal living must be restored unless ecclesiastical authority has established otherwise.

and also

Can.  1155 The innocent spouse laudably can readmit the other spouse to conjugal life; in this case the innocent spouse renounces the right to separate.

Hence, yes, the Church does encourage couples to reconcile, if that is possible. (That does not mean, of course, that the Church encourages victims of abuse to remain in abusive relationships; there are many other reasons why separation might occur.)