I think the only rational conclusion is that one cannot change the fate of Satan. But there is room for the idea that an angel that is "his" currently can change before the judgement into "not his" due to free will. And if that is the case, it could be an acceptable premise to pray for fallen angels or dark spirits. It fits with the theme of overcoming evil with good.
The second aspect we need to consider is what exactly is meant by "praying for"? I think the main focus of the debate comes back to Mat 5:
"Ye have heard that it hath been said, Thou shalt love thy neighbour, and hate thine enemy. But I say unto you, Love your enemies, bless them that curse you, do good to them that hate you, and pray for them which despitefully use you, and persecute you; That ye may be the children of your Father which is in heaven: for he maketh his sun to rise on the evil and on the good, and sendeth rain on the just and on the unjust." - Matthew 5:43-45 KJV
"Thine enemy" - this sense of enemy is also used in the parable of the wheat and tares to explicitly refer to the devil (cf. Mat 5:39), albeit by parable.
"Sun to rise on the evil..." - someone made the argument that this verse only refers to earthly beings because they interpretted "sun" and "rain" to be earthly effects. If that is the case, wouldn't that mean that you could include dark spirits like legion or other afflicting devils?
"Pray for..." - What exactly is meant by praying for someone / something? Jesus tells us how to pray, and the formula comes back to "God's will be done". This clearly means that the purpose of our prayers should never intentionally contrary to God's will. It's not as though we should pray for Satan to be pardoned from the fate that has been set out in scripture. Is it possible that praying for something isn't necessarily about changing the fate of that thing? Is there another purpose to prayer?
"That ye may be the children of your Father which is in heaven: for he maketh his sun to rise on the evil..." - it seems by this section in the passage that the purpose of prayer in at least some cases is not necessarily to "lock down salvation for the subject of our prayer". Prayer could be to express our nature as children of God by showing charity to those that are undeserving.