Peru finished their North America trip with two goals scored and nine conceded across four games, and the easy line is "they fade after the break". The half-by-half picture is messier than that. Six of the nine goals did arrive after half-time, but the Canada game was effectively gone at the interval, and against Colombia the first half was level before the game turned.
Here is how the four games went, from our match records. USA: 1-1 at the break, 1-4 at full time. Mexico: Peru led 1-0 at the break and it finished 1-1. Canada: 0-2 down at the break, 0-2 at the end. Colombia: 0-0 at the break, 0-2 at the end (still marked provisional in the DB). Peru's only two goals both came in the first half of their first two games, and they haven't scored in either of the last two.
The Colombia game is the most interesting one. Vavel's report has it scoreless at the interval, then Colombia's opening goal after the restart, and a straight red card for Miguel Araujo shortly after he came on. Colombia's second came in stoppage time. The first goal went in with eleven against eleven, which cuts against the idea that the red card was the whole story, though it clearly shaped the rest of the game.
What I'd keep from this is the Mexico game. It's the only one where Peru were in front at the break, and they conceded early in the second half there too. Whether that is fitness, substitutions or a team that doesn't know how to protect a lead is something these four results can't separate, and I wouldn't claim to know from the outside.