SAN DIEGO — A day after star closer Mason Miller threw his 98th pitch in a week while absorbing his first loss in a year, San Diego Padres manager Craig Stammen received an increasingly common question.As the Padres continue to find themselves in close games, how difficult is it to exercise restraint with one of the most valuable arms in baseball?“That’s the conundrum right there, is we’ve got the ace in the hole waiting down there, and we know that a lot of times when he’s able to pitch, the game is in good hands,” Stammen said before Wednesday’s 4-0 loss to the Los Angeles Dodgers. “But we also know he can’t pitch in 162 games, so we’ve got to manage both those things and do the best we can — what’s best for him for his entire career and also what’s best for us.”After overwhelming batters across the season’s first six weeks, Miller has issued six walks over his past five appearances. In Tuesday’s 5-4 defeat, the right-hander was charged with the first error of his career. Miller, who is averaging 101.3 mph with his fastball, has avoided any significant arm injuries since he sprained his right UCL with the Athletics in 2023.Still, more than two months before the Aug. 3 trade deadline, the Padres are exploring the market for relief help, league sources told The Athletic. The Padres have one of the sport’s best bullpens and more obvious needs for starting pitching and offense, but they are wary of overworking a bullpen that has fueled a 29-20 record and already might be feeling some strain — Miller in particular.Padres president of baseball operations A.J. Preller has a track record of doubling down on his bullpen. Shortly before the 2022 trade deadline, he acquired All-Star closer Josh Hader. Two years later, he landed top setup man Jason Adam and All-Star closer Tanner Scott within a span of three days. And last July, Preller made one of the most stunning deals of that summer, surrendering top shortstop prospect Leo De Vries as part of the return for Miller.The calculus this year appears more complicated. Kwanza Jones and José E. Feliciano, the couple who agreed to purchase the franchise ahead of next month’s MLB owners meetings, have indicated they are willing to spend money in pursuit of San Diego’s first World Series title. Meanwhile, after years of aggressive trading, the Padres have limited prospect capital to deploy amid what has been a season of bottom-five offense and patchwork starting pitching.However, relief is generally cheaper to acquire than, say, a mid-rotation arm. Potentially available names this summer include a pair of possible Hall of Fame closers: the Boston Red Sox’s Aroldis Chapman and Hader, now with the Houston Astros.The Padres have long been interested in Chapman, who at age 38 has a 0.51 ERA and 12 saves for the 22-27 Red Sox. The eight-time All-Star is one of the rare pitchers this century to maintain triple-digit velocity while staying healthy for more than a few seasons. Chapman is making $13 million, with a $13 million mutual option (and a $300,000 buyout) for 2027.Hader, in the third year of a five-year, $95 million contract, has full no-trade protection, but the Astros’ 20-31 start has made him a candidate for an eventual move. Sidelined by biceps tendonitis since spring training, the six-time All-Star began a rehab assignment May 5.Wednesday night at Petco Park offered the Padres bullpen a small reprieve. Shohei Ohtani homered on the first pitch of the game, the Dodgers scored twice more against Randy Vásquez, and concerning slumps by San Diego’s star hitters only deepened. A ninth-inning deficit also meant Miller and fellow high-leverage relievers Adam, Adrian Morejon and Jeremiah Estrada all received a full day of rest — the kind of break the team cannot reliably script.“You never want to take any success for granted, so we welcome all (potential) additions,” Adam said before the game. “But I like our group now.”Stammen pointed to the calendar. Additions or not, a crucial balancing act will continue for the rest of the season.“I think we felt really good about — even though it was a higher workload for (Miller) in April — that the games were spaced out enough that we felt comfortable using him in all those situations,” Stammen said. “And same thing with May and June and July and August.”— Chandler Rome contributed to this report.