The war occurred pretty late in the year so had they managed to postpone surrender about a month, the Sonderbund could buy time to reorganize during winter and canvas foreign aid. Depends on whether it snows enough to make the federal troops break off the campaign for a season.Don't take this for granted. There's a reason besides the lack of outside intervention in the war that ensured the very short duration of the conflict. Switzerland was not quite as simple as Catholic=Conservative and Protestant=Liberal. Indeed, one of the biggest issues in the Sonderbund War was that there was lots of unrest within the Catholic cantons over political reform, to the point that the liberal, federalized government was often able to undercut their enemies simply by promising better democratic assemblies within those cantons. Ticino in particular had a lot of anti-clerical Catholics who were strongly opposed to the war, IIRC.
My suggestion is you need a more violent civil war internally. Maybe Fribourg is sacked after it is occupied by the liberals, and the rest of the Sonderbund decides surrendering would not be in their best interests. Its sort of amazing that the casualties were as low as they were all things considered. More war crimes would provide postwar enmity that makes being a single state awkward.
Intervention of foreign troops seems more likely to backfire than help the Sonderbunds however.
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