It’s never said that they only love once in their life - but it said that they only marry once in their life, and the following passage makes me think that it’s likely that they only loved once:
For Dwarves take only one wife or husband each in their lives, and are jealous, as in all matters of their rights. The number of dwarf-men that marry is actually less than one-third. For not all the women take husbands: some desire none; some desire one that they cannot get, and so will have no other.
So, again, there’s nothing here that says that dwarves love only once. But it is stated clearly that they only marry once. The fact that some dwarves never marry because they cannot marry the person they wanted to marry originally is what makes me think that perhaps dwarves didn’t love more than once - or at least that it wasn’t often.
SOURCES: LOTR Appendices