I cannot, for example save the following search result.

http://buddhism.lib.ntu.edu.tw/DLMBS/search/export.jsp?q=涵宇海寬 OR 別山性在 OR 雲棲袾宏 OR 達觀真可 OR 無念深有 OR 儀峰方彖 OR 聞谷廣印 OR 無學幻 OR 憨山德清 OR 顓愚觀衡 OR 元白可 OR 大辯道焜 OR 見月讀體 OR 徧融真圓 OR 戲蘆澄心 OR 古雪真喆 OR 吹萬廣真&qf=TOPIC

You can't save from the search results page — if that's what you mean — because the site isn't using standard catalog software and there's no Zotero translator for the site.

You can hover over the save icon to see the translator being used, and you'll see it's just the DOI translator on all pages of the site, because for some reason they include a DOI in the footer of all pages. Zotero picks that up, but it's not a DOI that's registered in any of the DOI registries that Zotero checks, so the save fails. (For me it falls back to saving the search results as a webpage. I'm not sure why that's not happening for you, and I'd want to see a Debug ID from the connector for such a failure to debug that, but a webpage item isn't that useful here anyway.)

On an individual article page that does include a DOI, you should get the article itself as an option and be able to save that (again, assuming the DOI is registered in one of the main registries). On article pages that don't include a DOI, it'll just try to save the DOI at the bottom and fail.