(A) を限りに is an expression used to indicate the time that something ends or significantly changes. (A) is usually a time expression. 限りで is less formal compared to を限りに. This phrase often follows words like 今日、今回、今月、今年 and so on.
を限りに is also used in a set phrase「声を限りに」- "to the limit of one's voice" or "at the top of one's lungs" as in 「武は声を限りに叫んだ。」- "Takeshi screamed at the top of his lungs." It can be also written as 声の限りに