Hi babylocks. Your peeps sure sound like they're having a rough time of it.
I must admit that there have been a couple of times where I meant to check the refrigerator to make sure I had at least 500 food in there for the night and realized when I opened the game in the morning that I'd forgotten.

The peeps were starving, extremely weak and took almost 2 days to fully recover.

There must always be food in the refrigerator.
You can keep an eye on a peeps health by looking at their Health Status bar by clicking the Detail button. If it's 3/4 full and your peep was recently ill and cured then the bar should start filling back up. If it's 1/2 full and they were recently sick and cured give them some hand sanitizer, fruit, etc to increase their health and check them again within 30 minutes. (You can do a Doctors Consultation if you want.)
If you don't see a good improvement then they may have an infection that requires 1 or more medications. This is where you really need a Doctors Consultation. Pay close attention to the information in the Dr. Consult. A peep's status may no longer say "Sick" after giving them just one of the medications listed on the Consult. However, they will not be completely cured and their health will continue to decline unless you give them ALL of the required medications.
How are they doing money-wise? Do you have enough saved for Doctor Consultations if they become necessary?
Good luck! Here's wishing a healthy future for your peeps (a nickname for my little virtual family members).
