Likely to be the flys I would have thought. If our girls wriggle out of their masks then they often have runny eyes by the evening. Wish they would just keep them on, it is for their own good after all!!
Id use a mild saline solution and cleanse it twice a day, stick a fly mask on if you can or a fringe, pardon the pun, but do keep an eye on it as they can become infected quite quickly. At this time of year it could also be an allergy or the sun .....but most likely flies .