This is "Stasis", S06E09 of The Outer Limits (1995-2002).
From the The Outer Limits Wiki:
In a future world of scarce resources, the world government regulates the population into two working classes (Alphas and Betas) in order to maximize conservation. These two classes rotate in and out of suspended animation for 72-hour periods. But what happens when an Alpha and a Beta fall in love with each other and never see each other face-to-face except for shift changes?
The story is set in a futuristic society where workers are divided into two groups who take turns going into suspended animation for 72-hour periods. There's also a class of people who manage this system and aren't required to go into stasis themselves, referred to as the Elite.
The main characters are a man and a woman who share the same quarters and work in the same role, maintaining infrastructure such as control valves. They leave recorded messages to update one another on their progress, and only see each other in person, briefly, when it's time to switch places in their shared stasis pod, which is located in a large communal area occupied by many such pods.
They develop feelings for one another, and express this through their recorded messages and by leaving things (such as candlelit dinners and roses) for each other in their shared quarters, but feel the need to hide this from everyone else due to the oppressive nature of their society.