Don't see how Cuddy ended up alone on the prarie. Or... (Spoilers).

She was thirty one. The older you get the harder it is to have children. She wanted Giffen, he left town to go get himself a wife instead. He considered her too plain and bossy.

Same for Briggs, he had a farm life earlier in the book and didn't like it, if a claim jumper deserter of the army didn't want her, I guess she felt weak for once. If she didn't find a husband eventually she would break her body on the farm and be an old maid.

Also keep in mind she was not like everyone else. She was head strong and did not conform to the lesser state of womanhood like everyone else. In the book she has an older friend who teaches with her, as soon as she got a proposal she high tailed it out of there.

also, remember she had just lost her virginity to briggs. that pretty much ENSURES that no one else will marry her in those times.

She hadn't really struck out on her own in the sense of isolation -- yes she had her own farm and land and income from it, but danger-wise she was close-in to the little town she belonged to, and people came by from there on a regular basis.

I'm no expert but I have a passing interest in some of the written experiences from the pioneer days, and although it was more usual for every woman to seek a husband for practical purposes, there were case of women just being independent as long as they had some kind of asset, like a farm. They just had to make sure they were armed -- much of this early necessity is why there is still such strong feeling about gun ownership to this day -- back then it was a necessity especially for those in vulnerable positions.

Many women who were widowed simply had to carry on that way; since nobody wanted her she just did it anyway without being a widow first.

It does seem slightly unlikely that she would be so rejected, as from what I read, most men out there didn't really care what the woman looked like or acted like, they just took any wife they could get, similarly for practical reasons.