Well according to Xanathar's Guide to Everything's 「This is your life」 p, they can indeed have children . There are three tables in XGtE, ...
不过：
As noted in another answer (hat-tip @Akixkisu), Xanathar's Guide to Everything allows all four combinations of parents, but that book is setting-agnostic, so you might rule that the setting-specific books take precedence (noting that the question is tagged Forgotten Realms.)这是说【Xanathar's Guide to Everything】不是[规则]。
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SO：
按2E（PHB 30）来说
1） 任何同时拥有精灵和人类祖先的人要么是人类，要么是半精灵（精灵只有精灵祖先）。2） 如果人类祖先比精灵多，那么这个人就是人类；如果有相同数量或更多的精灵，这个人就是一半精灵。
而到了 (AD&D 2e)【Forgotten Realms Campaign Setting Box Set Revised】 p.12
半精灵可以交配和繁殖，但总是会产生另一方父母的后代（半精灵-精灵配对会产生精灵的孩子，而半精灵-人类配对会产生人类的孩子）。第二代半精灵只有在两个半精灵结婚的情况下才会产生。Is the offspring of an elf and a half-elf an elf or a half-elf?
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 marry.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.
