SO, basically, Digimon World has an in-game clock, and Digimon that you have can only stay awake for so long (Depending on the Digimon you have as well). Specific Digimon to recruit require you to wait for certain times for them to appear or be available for recruiting.
The absolute BIGGEST offender, at the current time, is the sea monster known as Seadramon:

Seadramon not only requires specific time frames to work with, but before you can even come close to recruiting Seadramon, the following things need to be done:
-Either recruit Angemon, talk to Tankmon in Toy Town, or recruit Shellmon. Shellmon's the easiest since it doesn't require you to have a specific Digimon. After doing any of these three tasks, you will hear rumors of Seadramon's presence in Dragon Eye Lake.
-After that, or before that, obtain the Amazing Rod from ShogunGekomon for 300 Merit Points. Sounds simple, yes? No it is not. You have to first acquire a huge ton of cards that you can exchange for Merit points, some cards being more valuable than others. After this tedious task is done, claim the Amazing Rod for yourself.
-Purchase Meats to use as Fishing Bait from the item shop. Given what all you've had to have done to get to this point, buying bait is not going to be a problem.
-Head to Dragon Eye Lake, in the southern most portion of Native Forest where you essentially have a horizontal view of said lake.
After this, you think you're ready to fish up a sea serpent, yes? HOWEVER, Seadramon appears RANDOMLY and ONLY during the Morning or Afternoon, meaning depending on how much time your Digimon can stay awake, you'll probably be working to try and fish Seadramon at only a single one of those times of day. Also, when Seadramon DOES spawn, you can't miss him. Literally, he's so big you'll never mistake him for any other fish in the lake, plus his movements are more snake-like. Now the REAL problem after all of this nonsense, though, is reeling in Seadramon once you get him on the hook. Seadramon is VERY easy to lose grip on for rather obvious reasons, but here's the trick; STALL LIKE HECK when trying to reel him in. After several minutes, Seadramon will begin to tire out, and that my friend is when you reel him in and the giant Seadramon appears before you. To recruit Seadramon, you have to Befriend him out of the three options he gives you (You can either learn a new technique OR get an item that allows your Digimon to become Seadramon). If you befriend him, Beetle Land becomes accessible at any time of the day, and recruiting all the Digimon there is an absolute joke when compared to whatever nonsense you're put through in the game.