This is what Tolkien says
'When Denethor became Steward (2984) he proved a masterful lord, holding the rule of all things in his own hand. He said little. He listened to counsel, and then followed his own mind. He had married late (2976), taking as wife Finduilas, daughter of Adrahil of Dot Amroth. She was a lady of great beauty and gentle heart, but before twelve years had passed she died. Denethor loved her, in his fashion, more dearly than any other, unless it were the elder of the sons that she bore him. But it seemed to men that she withered in the guarded city, as a flower of the seaward vales set upon a barren rock. The shadow in the east filled her with horror, and she turned her eyes ever south to the sea that she missed.
'After her death Denethor became more grim and silent than before, and would sit long alone in his tower deep in thought, foreseeing that the assault of Mordor would come in his time. It was afterwards believed that needing knowledge, but being proud, and trusting in his own strength of will, he dared to look in the palantír of the White Tower.
To me "loved her in his fashion," doesn't sound like a great love. I think love came hard to Denethor and he wanted to own those he cared for. I think he was kind to Finduilas, but rather domineering.
My own theory as to why Finduilas died is that sea longing and depression wore her down and made her easy prey for some mundane illness or disease.
I don't think her death had anything to do with Faramir's birth or a later stillborn child. I think if Denethor had blamed Faramir for killing his mother, he would have mentioned it in their bitter exchanges. In my head canon, Faramir with his sensitive nature, reminds Denethor of Finduilas. I also give him her eyes and hands.
In my personal head canon, she might have lived had she been sent to Dol Amroth when her health started to decline.
Being British, and living on an island, I believe sea longing is real(though certainly not fatal), as many Britains feel melancholy if they cannot visit the sea at regular intervals.
What do others think? I thought this might be a fun topic to discuss.