Something crossed my mind in the past couple days:

In addition to keeping track of the month and
week, the game also keeps track of the days and
hours.

Now, since you can actually sit and let the hours
pass while you're roaming the town or at your
ranch, that implies to me that it does have SOME
sort of effect on your monster.

Now granted, it may just be something that's been
done for "realism", but I doubt it. If hours and
days of the week didn't matter, there would be no
time passing in the game. Our monsters would roam
the farm and town in a perpetual daylight.

But yet we're able to watch day turn to sunset,
turn into night, watch the day change at the
stroke of midnight, and then watch the sun rise.

This implies to me that there may be an "ideal"
time to raise monsters. (And I'm currently doing
some research to test this theory, in between
charging after my goal of actually beating a
Monster Rancher game in its entirety.)

Has anyone else looked into this as well?

The guide has said nothing about it.

The only thing I ever really noticed is that when you fire up the game, the time will match your system time.

I have always chalked it up to being a time limit on poking around your farm looking for items.

I do know you can waste a whole week in town. When
the last hour of the last day comes you will be
forced back to the ranch, on the next week.

Interesting, Nox. I hadn't bothered seeing what
happened if I just left it sit for a whole week
yet.I mean, it makes sense that you'd be forced
back to the ranch, but I was unaware you'd lose
the opportunity to do an action if you waited too
long.

Thorr-
The reason why I think there's something more to
it is that time pauses when you're actually in a
menu. When you go to train, the time pauses. When
you choose to feed an item to your monster, time
pauses. When you buy from the shop, time pauses.
Time also pauses when you're without a monster.

Since the smallest time period we know has an
effect is which month you're in, it makes me
wonder why it pauses if there's nothing important
in the day of the week or the hour.

Still, you might be right and I might be simply
digging into pure minutiae, and looking for order
in the random..still no harm in looking though.

Well, when time passes, weather can change. Weather does influence training. But as I said, the guide (which is meticulously detailed) never says anything about time or day of the week.

The only thing I can think of is limited time to find items on your ranch..

But.. it seems it moves so slow. I had to forget about the game for a half hour or an hour or something for the week to end without me doing anything.

Right, Shen, that's the thing. It's awfully long
if the whole point of time is to limit the amount
of items a monster can find. I'd think there would
be other more efficient ways of handling that, if
they were worried about abuse.

The developers at Tecmo seem to almost expect a
certain amount of game breaking from people who
get addicted, whether it's the use of a "perfect"
training regimen to never rest their pets or some
other tactic, they don't seem to mind people
finding ways around the limitations that they set
up within the game. The only sort of thing they
seem to be trying to prevent is the reset method,
and I'd wager that's due to the online component,
especially with the total stat cap being included.

For other games, sometimes you can close the DS top and it will pause the game indefinitely. It seems to pause in MR (the screen/sound still go off), but the time still passes.
I, assuming it would pause it, closed the DS and came back to the "A week has passed!" message. :|
Just fyi.

Also, I selected Quit and reloaded and it was a day later. Quit again, and loaded and it was Wednesday. Quit again, waited an hour or two, reloaded and it was Saturday. I have no monster, so I have no idea why this is :| (was messing around with combining).

My guess is that the day advances once every time you quit, so
even if you try to reset in spite of botched combo results, if you
reset seven times a week will pass.

The time is directly related to your system time.