XGtE suggests that you are free to make it up.
Ideas, not rules (XGtE, 61):
Even though these pages are full of tables [...] they don't make up a
rules system - in fact, the opposite is true. You can use as much or
as little of this material as you desire [...] For instance, you might
not want these tables to help you decide who your parents [...] are,
because that's among the information you've already come up with.
The Nonhuman Parents table (XGtE 62) shows that it is possible for a half-elf's parents to be both an elf and a half-elf:
If your character is a half-elf, [...] 6 One parent was an elf and the
other was a half-elf.
So it confirms that that half-elves and elves may have half-elven children, but that you are free to decide either way. As 5e lore doesn't go into more detail you may borrow inspiration from other editions if you do desire to do so.
3.e says (Races of Faerûn 58):
Half-elves have at least one elven parent or grandparent, or two
half-elven parents. To put it another way, the child of a half-elf and
a human will be human, unless the half-elf parent was the child of a
full-blooded elf. Unless a half-elven line marries into other elven or
half-elven families, their elf characteristics fade in a generation or
two. On occasion elven traits can reappear in otherwise human children
born several generations later, but half-elves of such remote descent
are very rare.
2e says (PHB 30):
1) Anyone with both elven and human ancestors is either a human or a
half-elf (elves have only elven ancestors). 2) If there are more human
ancestors than elven, the person is human; if there are equal numbers
or more elves, the person is half-elven.
(AD&D 2e) Forgotten Realms Campaign Setting Box Set Revised p. 12 phrases this more concise and less ambigious:
Half-elves may mate and breed, but will always produce the off-spring
of the other parent (a half-elf elf pairing will produce elven
children, while a half-elf human pairing will result in human
children). Second generation half-elves only result if two half-elves
These older editions strictly denote that elves have only elven ancestors, that means at least one parent has to be a full-blooded elf to give birth to an elf when mating with an elf or a half-elf, but no such restriction is a confirmed part of the 5e lore.