I guess I'm thinking of it more from the perspective of someone who is so used to having phone signal, not hearing from someone for a day would send alarm bells ringing.From what I've seen, there was no mobile signal at the refuge. But if she had continued her planned route the next day, then within 30mins of leaving the hut, she would have reached an area with mobile coverage.
He will not have known the extent of the mobile signal coverage and it's not unfeasible that she could be walking in an area without signal for a day or two.
The past tense is probably a bit of a red-herring at this point. It was a good 2 weeks from her going missing, very unlikely anyone would survive that long. So he will have been dealing with the likely prospect she had perished on the mountain. If he'd referred to her in the past tense a day after she went missing, that would be different. The other possibility is he had fallen out of love with her a long time ago and it was just a truthful slip; that alive or dead, he didn't love her anymore.
Maybe they were used to it having been travelling around Europe for so long?
It's such a sad scenario, whatever the final outcome.