Going through about 13 pages of my library research notes I find certain inconsistencies or conflicts in the various accounts of the military manuevering and fighting during the summer and fall of 1777. There are a couple of notes that indicate Asa was or might have been involved in the Battle of Stillwater, sometimes called Second Saratoga. I don't think he was. It took place on October 17. I think he was on his way back home by then.
General Stark occupied Fort Edward at the south end of "The Great Carry", which is the ancient 11 mile portage between the Hudson River and Lake Champlaign, effectively bottling up Burgoyne so that he could neither retreat back north nor obtain provisions or reinforcemnts from that direction. I don't know what troops Stark used for that operation. Asa could have been there.
Here is the situation on September 18, 1777: General Burgoyne's forces are trapped. The climactic Saratoga battles are about to begin. Just over a month before the New Hampshire Militia had crushed the Germans and English at the Battle of Bennington. General Clinton of the Continental Army wanted their help, but their three months enlistment expired that day. What would the militiamen do? Here is the account of one who was there:
"The army was animated by the arrival of a band of citizen soldiers who had conquered the Germans and killed their commander near Bennington; but the term of service for which these men were engaged expired with the day, and every exertion was made to enduce them to wait the event of an action, which was daily expected; but to the exhortations of the comander-in-chief (Clinton) and the persuasions of many other officers, no decisive reply could be obtained.
General Stark and his subordinates '...thought it proper and necessary that they should adhere to the service...' But I observed that they employed no influence to promote that end, which was, in effect to discourage it.
The men communicated with each other in whispers and a buzzing was heard around their campfires; for they had neither unpacked the baggage which they carried on their backs, nor laid down to repose. I left this band of hardy freemen about 11 o'clock, determined to watch the result and about 5 minutes after 12, I discovered them in motion, the aid-de-camp of the General called for the parole, to pass the guards of the camp, and I verily believe neither officer nor private was left behind; nor could they have been beyond the sound of action when it began, yet not a man returned.
This punctuality of the father, the husband and the son, who till their own ground and enjoy the sweets of domenstic life, is not reprehensible, since it is enjoined by an irresistible impulse of nature. These citizens had fought once, and having served the term of their engagement, were desirous to tell of '...feats performed...', and look into their private affairs, after which they were ready again to take up arms."