daily calorie intake--puzzled

The following is my current opinion.

I've been reading various topics on this board...enjoying them all... but am puzzled about something. I read a lot about how not taking in enough calories everyday could result in no weight loss or even a weight gain

Unlikely to be true in most circumstances/contexts.

and that you should increase your calorie intake to break the no-weight-loss routine.

This is sort of blanket advice that gets handed out without considering context. In my opinion it is wrong far more often than it is right.

So, how come someone who has had a gastric bypass or other weight loss operation, loses weight afterwards by intaking a very limited amount of calories?

Because that's how it works and the previous things you heard are likely not how it works in most situations/contexts.

Also, how about the people who are following a very low calorie diet consisting of drinking shakes while under a doctors care... they lose weight consistently.

Same answer as above.

I know they are under a doctor's care during this process, but unless the doctor has a magic wand that he waves over these individuals, shouldn't they stop losing weight because of a low calorie intake?

Nope. And that's the interesting part. When calorie intake is actually tightly monitored, calorie deficits result in weight loss.

....just trying to understand why I keep reading that eating too few calories results in no weight loss when in fact, those under doctors' care seem to lose quickly and consistently...

I'm under the belief that attempts to create large calorie deficits tend to result in remarkably poor adherence and inaccurate logging. Now having said that, I also think there's merit to the idea that energy intake can effect energy output, and reducing calories quite low could in theory result in lower energy expenditure whether that's due to involuntary or voluntary activity changes.

Now, in some cases there may be merit to attempt to gradually increase energy intake over long periods of time to attempt to upregulate hormones (either through a straight-up diet break or in some cases a long reverse diet). Anecdotally, I'm seeing a slightly higher maintenance intake after a successful reverse myself -- but I think context needs to be considered.

What you tend to see on MFP forums is lack of context, and people throwing out "eat more" without first looking at the individuals stats, whether or not they use a food scale, how accurate they log things, whether they've already lost a bunch of weight (adaptive thermogenesis), leanness, duration of caloric deficit, etc, etc,

So you have to consider these things before throwing that out there. My general observation is that it seems like more often than not, the answer is not to raise intake. TYPICALLY I see tracking errors and failure to measure properly resulting in energy intakes being significantly higher than what they assume -- although once again context is everything and the real take away is to gather that context before dishing out what could be absolutely awful advice.