Loneliness is one of Frost's most profound themes throughout his poetry. I think the best place to begin discussing this theme is with one of his most famous poems called "Stopping by Woods on a Snowy Evening." In it, the speaker has come to a halt "on a snowy evening." He is riding his horse and the sense is that he's just stopping to take a break and listen. He doesn't hear much, except for the horse giving his "harness bells a shake.../The only other sound's the sweep/ Of easy wind and downy flake." At the end, the speaker says:
The woods are lovely, dark and deep,
But I have promises to keep,
And miles to go before I sleep,
And miles to go before I sleep.
We don't know where he is going, but it doesn't seem as if he's going home to someone. He's not necessarily lonely, but he's certainly alone.
Many of Frost's poems have this feel to them. Some are set in homes and farmsteads that are far from other people. Examples are "Mending Wall," in which two men meet once a year to mend the wall between their farms, and "Out, Out" in which a young boy is killed in an accident involving a saw. A doctor gets to him, but not in time, establishing a great distance between the people in the poem. Another example is "Home Burial" in which a family has buried their young child in their backyard, far from town.
The sense of distance that Frost creates in his poetry allows for the sense of loneliness of which you speak.