Hi @Susanother,
It is really difficult when you are in a "damned if you do and damned if you don't" situation and are trying to weigh up what the best decision would be. Getting a response like that can be hard, as not only can it be bruising to you but also makes it difficult to decide what way forward is best.
It does sound as though when your friend is going through a difficult time that they tend to withdraw socially, which can be a common symptom of many mental illnesses. It is great that you are still persisting to let your friend know that you are thinking of them, when many people would have walked away. This is a great sign of your compassion and loyalty.
An idea may be talking to your friend once this difficult period has past and discussing what they would like during the times when they are unwell. This may help you to know what to do if this occurs again in the future.
In regards to what to do now, it definitely is a hard decision, particularly when you feel as though you are doing the wrong thing regardless of your actions. Maybe a way to think about it would be, if your friend is going to be upset/angry/annoyed/etc regardless of what you do, what would you feel more comfortable with doing? If you feel as though contacting your friend again to let them know you are here for them when they need, then great, if not and you feel that you would prefer to let them deal with this in their own way and contact you when they are ready, then that is great too.
In trying to manage what would be best for your friend, dont forget to also check-in with yourself about what is best for you 