Further Evidence that the Ability Score Increase Racial Traits are a One-Time Bonus
PHB 11 (empahasis mine)
Your race also increases one or more of your ability scores, which you determine in step 3. Note these increases and remember to apply them later.
The rules state your race will increase your ability scores that are determined in step 3. It says nothing about increasing them with the standard occasional level increase of +2.
Later in step 3... PHB 13
Now take your six numbers and write each number beside one of your character’s six abilities to assign scores to Strength, Dexterity, Constitution, Intelligence, Wisdom, and Charisma. Afterward, make any changes to your ability scores as a result of your race choice.
After you assign your ability scores, you adjust them based on your racial traits. Again, no indication of changing them at any other time.
PHB 15 (Beyond 1st Level)
When your character gains a level, his or her class often grants additional features, as detailed in the class description. Some of these features allow you to increase your ability scores, either increasing two scores by 1 each or increasing one score by 2. You can’t increase an ability score above 20. In addition, every character’s proficiency bonus increases at certain levels.
Only class is referenced as granting additional features with leveling up. There is no reference to racial traits in connection with going up a level. Aside from Dwarven Toughness I can't think of any racial trait that increases with level, though I may be overlooking something esoteric.
PHB 20 (emphasis in original text)
Ability Score Increase. Your Wisdom score increases by 1.
Dwarven Toughness. Your hit point maximum increases by 1, and it increases by 1 every time you gain a level.
These Hill Dwarf traits provide the clearest insight into the RAW. The first trait, Ability Score Increase states your wisdom score increases by 1. This means it increase one time at creation, by 1 point. The second trait, Dwarven Toughness, is clearly intended to provide an increase with every level and this is clearly stated. Your hit point maximum increases by 1 every time you gain a level. Every racial ability increase is stated the same as this one, and makes no mention of any increase with level.
As stated in a previous answer, the PHB makes no reference to racial ability score increases in any of the Ability Score Improvement descriptions for any of the classes (PHB 67, Druid, for example)
The complete omission of the racial ability score improvement trait at all points in the PHB that discuss Ability Score Improvement with level make it quite clear that racial traits do not provide ongoing improvements to ability scores. They are a one time bonus at character creation.