Sam and Smeagol

[MLD-Grounds-Keeper-Willie]

Gollum lost trust in Frodo when he was betrayed into the waiting arms of Faramir. That was a terrible set back.

In defence of Frodo here, Frodo actually saved Gollum's life. Gollum thought he was betrayed, but really wasn't. It's a minor detail at first glance, but it is actually much bigger. Yes Gollum did think that Frodo betrayed him, but after, Gollum realizes that Frodo has indeed saved his life and protected him. So then Gollum, goes to Frodo and begs Frodo to save him:

We will promise Master, if he saves us. We'll promise to It, yes.' He crawled to Frodo's feet. 'Save us, nice Master!'

So, I think that this actually strengthened the bond between Frodo and Smeagol, and Smeagol has a lot more trust in Frodo. So, without that, it seems it goes like this:
+ Frodo's pity and love
+ Frodo saving Smeagol from Faramir
- The ring
- Sam, especially at the Stairs of Cirith Ungol

So, I find that Sam had a huge part in Gollum not repenting.