Despaigne lasted three innings in Friday's 10-0 setback to the Nationals, allowing seven earned runs. In his last two starts, he's allowed 15 earned runs.
"If you look at his season, it's been a little Jekyll and Hyde," Black said. "Everyone remembers the most recent [start]. It was rough. The last two haven't been what we expect out of him."
Black was unsure when Despaigne's spot in the rotation would come up.
"We don't know where we're going to slot him in for his next start. With the off-day Monday, we can do a few things with the rotation," Black said.
Despaigne has pitched well at times, limiting the D-backs to one run in seven innings on April 14 and then allowing two runs in 6 2/3 innings on the road against the Rockies.
There's always the possibility the organization could change its mind on Despaigne, who is filling in for an injured Brandon Morrow, before his turn rolls around.
Morrow, on the disabled list since May 5 with inflammation in his right shoulder, played catch for the first time on Friday. He's not expected back soon.
Black said that Morrow will likely need one, if not two, rehabilitation starts in the Minor Leagues before jumping back into the rotation.
If the Padres opt to go another direction, they could turn to lefty Robbie Erlin, who is pitching with Triple-A El Paso. Erlin, 24, has a 5.15 ERA in seven starts at El Paso, though he has pitched well in four of those starts.
The Padres could make a bold move and promote 24-year-old right-hander Colin Rea from Double-A El Paso. Rea is enjoying a breakout year with Double-A San Antonio, posting a 1.17 ERA in seven starts with 32 hits allowed and 43 strikeouts in 47 2/3 innings.
Rea isn't on the 40-man roster, so the team will have to remove a player to make room for him.