[noun] + を限りに、[sentence] [noun] + を限りとして、[sentence]
を限りに goes after a time word or an occasion and makes it the last one: "as of today", "after this time, no more". What follows is something that stops – a habit you quit, a shop that closes, a job you leave. It is formal and firm, the language of announcements and resolutions.
The noun is a point in time: きょう今日, ほんじつ本日, こんかい今回, こんげつまつ今月末, こんねんど今年度. The day itself is included; it is the last day, not the first day of the change.
In こえをかぎりに声を限りに, "as loud as your voice will go", 限り keeps its older meaning of "limit". It goes before a verb of shouting or calling, and has nothing to do with an ending.