Given there is a risk of being thrown into a mental asylum, I think you may have to be a bit harsh.
Let's get this clear. You have clinical depression. While it is hard to understand, the best and easiest thing to do is to give you your space. Let you be a little bit on your own, give you time. Room to breathe, if you will.
It is horrible that your family does not understand that. My wife's mom admitted my wife in the psychiatric hospital because she was having a manic breakdown. My wife suffers from severe bipolar disorder and anxiety.
What my mother in law had to say to that was: "I was looking out for you, I wanted the best for you". My wife tells me all the time: "I'd rather spend the rest of my life in prison than be a single day in the mental hospital". She HATES that place.
If they've already considered throwing you in one of those hellholes, you need to tread VERY carefully. Anything in the lines of "oh I was feeling a bit low.." would automatically mean, "Welp, off you go to the psych ward". It might not be that extreme with your family, I am exaggerating for dramatics. But still..
A few directions you go:
1. Make up for not talking much or for your prolonged silence:
My brother has bipolar disorder too and he hardly talks to my(/his) mom. He is a sly sneaky guy. This is what he does:
- He doesn't talk for months.
- When he finally feels like talking and decides to talk, he talks for hours! Literally, hours. My mom gets on the phone with him and talks to him for 2-3 hours.
What does that do to my mom? She feels really happy and satisfied. Of course, the call started with a lot of frustration from my mom. "Why didn't you call for so long? What is wrong? Why do you hate us" kind. But he just gives some random excuses/lies and then starts talking about his life in general, gets my mom excited about things. The reason he doesn't just tell her he does not feel like it because of his mental state is not because of the fear of being thrown in a mental hospital. I am Indian and in India, mental disorders are not a thing. No one recognizes that as an actual disease. If he says that he has bipolar disorder, my mom would probably say "no you don't, stop making stuff up." OR "Just call us and talk to us, you will feel happy". So, he does not even try to explain all that to them and just make them forget about his silence.
If you think you will never be comfortable enough to talk for that long or if you feel like they come to you and act pissy to you about you not talking BEFORE you could get comfortable enough to talk for a long time, take a look at the next option:
2. Come up with something better than empty promises:
I don't know how good you are at lying, but you may want to work on your lying skills. Going back to my brother's behavior:
If he does not feel like talking and it has been a few months, he has to say something so my mom would stop calling him 20 times a day. What does he do? Calls her up and makes something up and hangs right back up. Few examples:
I am in the middle of a shoot mom, I will call right back up.
My cat is sick, I am at the vet's hospital. I will call you back in an hour.
You get the idea. Something that will get you off the hook for that instant. But then of course, you are expected to call back in a week or so at least. No one spends an entire week at the vet's.
Nothing that indicates your mental health is an option here. So that narrows down our options!
Nothing like this:
I've been feeling a bit low for the past few days
I need some time to think stuff over
I am going through a difficult time right now
Here are a few more masterpieces my brother has used so far:
I was going for a run and my phone fell off my pocket and into a puddle. I've not been able to afford a new one.
There was heavy winds and the electricity pole outside our house broke, so I haven't had power (and yes, he said he didn't have power for literally 2 months).
My cat died, so I needed time to get over that sadness (his cat actually did die, but he recouped from that in a week and spoke to ME, just not to mom).
I was in the forest for a shoot, so had no cell reception.
I've just been really busy at work/school. I've been having a hard time understanding something/I have a very tight deadline on something.
A lot of these are a bit over the top and my mom knows it. My brother just doesn't care. These are excuses they cannot deny. It is YOUR story, YOUR life. They cannot say it is not true, they don't know it.
You didn't mention how old you are in the question, so I do not know who you live with or what your current occupation is. So depending upon that, you may want to change these a bit.
Some times, my brother does a preemptive lie routine. Where he calls my mom up out of the blue and tell her that he has an important assignment and won't be able to talk for a few months because it is off the coast of China. That could come in handy.
Also, the one thing that REALLY helps:
Whenever you get out of your depressive state, take the initiative and call them without them asking you to. Just pick up the phone and talk to them in a happy note. Make them feel important to you and that you thought about them. This eventually starts feeling like a chore, but this will make absolutely sure they know you still love them.
Honestly, telling them the truth is not going to be an option for you and telling them you will keep up with them more in the future isn't either. The best you can do is make sure they still like you and accept that you just don't talk to them as often as they want you to.
Do whatever it takes to ensure that and I think that will help you have your room.