The hold spells paralyse, levitate does not
The main difference I can see between hold person/monster and levitate is that the former paralyses the target, whereas the latter only lifts the target upwards.
From hold person (PHB, p.251):
The target must make a Wisdom saving throw or be paralyzed for the duration
And hold monster (PHB, p. 251):
The target must make a Wisdom saving throw or be paralyzed for the duration
Compared with levitate (PHB, p. 255):
One creature of your choice that you can see within range rises vertically, up to 20 feet, and remains suspended there for the duration [Concentration, up to 10 minutes] ... An unwilling creature that succeeds on a Constitution saving throw is unaffected.
A creature affected by levitate can still do many things, including making ranged attacks and casting their own spells that require saving throws, whereas someone who is paralysed can do nothing.
From the Paralyzed condition (PHB, p. 291):
- A paralyzed creature is incapacitated (see the condition) and can't move or speak
From the Incapacitated condition (PHB, p. 290):
- An incapacitated creature can't take actions or reactions.
Since a paralysed target is a sitting duck, it seems much more fair to allow them to make a saving throw each round to recover from this, since they have no other options; someone affected by levitate, on the other hand, can still do many things, just nothing that requires melee range or (depending on the room, since you can apparently move yourself around if you can "climb" along the walls/ceiling) movement.
So I'm concluding that, because the effects of hold person/monster are more severe, the target "needs" to make a save each round more so than someone affected by levitate.
Duration
The other consideration, however, is duration. Hold person and hold monster both last a minute, whereas levitate lasts for 10 minutes. Therefore, if someone doesn't really have a lot of options (for example, if a melee-focused character who has, say, run out of javelins) is potentially stuck in the air for 10 minutes, that will take them out of the fight for longer than someone who is paralysed (if they have literally no other options to contribute), although they will at least not be as vulnerable as someone paralysed (i.e. they can take the Dodge action, as Theik points out, imposing disadvantage on attack rolls against them, compared to the advantage and auto-crit imposed by the "paralyzed" condition).
That said, most combat doesn't last more than a few rounds, so in a typical combat, this will never be a concern. I'd still lean on the side of suggesting that allowing a saving throw each round for levitate would weaken levitate.
What about a Strength check rather than a Constitution save?
Another idea could be, rather than following the example of hold person, perhaps borrow from entangle or similar? Being held in the air against your will, whilst it doesn't actually restrain you with regards to the "restrained" condition, does effectively restrain a melee-focused character. Entangle restrains one or more creatures as per the "restrained" condition, and provides a different way to end that condition.
If someone affected by the levitate spell were to be allowed to use their action to make a Strength check to break free of the caster's hold on them, this might be more balanced; they'd still have to burn an action, rather than getting a "free" saving throw, but it does still give a melee-focused character suspended in mid-air an option to do something about it.
For reference, here's entangle (PHB, p. 268):
A creature restrained by the plants can use its action to make a Strength check against your spell DC. On a success, it frees itself.