This has always bothered me too. Who convinced them to stop? They were two young girls without many resources - no car no credit card, etc. Just kids missing, with a planned pick up time, and on seemingly good terms with their parents/guardians.
I just don't understand who could have or would have convinced LE that the girls weren't in any danger.
MOO
I think some of this may be attributed to some small town optimism. (Or perhaps even naivete.) At that point nobody thought they were dead. They were probably feeling pretty optimistic that the girls were okay. They thought they may have been injured in the park, but when after several hours the search yielded no results IMO they then concluded that the girls simply weren't there. Protocol SAR in my region is to consider the safety of the searchers. SAR people are wonderful, and you have to force some of them to stop, but they have families as well. I have sat up many a night worrying about my husband. I believe they reached a point where the searchers' safety was at risk so "officially" the search was called off. That doesn't mean people stopped looking.
Two little girls don't get murdered every day in Delphi. There is usually another explanation: went off with friends and got stranded, going someplace where they're not meant to be, staying out too late and are now worried they'll get in trouble...all of those are better considerations than homicide. If my child went missing I'd HOPE it was one of those things. Even really "good" kids with no prior history can make poor choices. My kids are totally awesome-polite, smart, good grades, good listeners, etc. And yet sometimes they'll do something out of left field and I'm like "Who ARE you?" These are children we're talking about, as smart as they are, there is still some developing to do.
IMO once they didn't find them in the park then there were other avenues to check: hospitals, friends' houses, social media accounts, cell phone pings and records, even other police depts in case there was an accident. Point being, when the girls were not found in the park, assumption was probably made that they were no longer in it. It wasn't as though LE was like, "Well, it's too dark, let's all go home and play Candy Crush. They're probably fine." There are many things to be done when a child goes missing; looking in the immediate area is just one part of it.
Finding them on the evening of the 13th rather than the 14th would probably not have made a difference. LE has said that the crime was quick. There IS a chance, though that continuing on could have contaminated a crime scene if there was one. At that point in time, though, I don't think anyone (including the families) thought a crime had been committed.