Will putting an oil painting under glass cause damage?
As long as the Painting isn’t recently painted, within 6-12 months, then there isn’t a general consensus and the answer is: It depends.

The reason for the delay after the painting is finished is that it can take this long for the painting to fully 'dry'. In your case, this isn't a consideration.

One of the biggest threats to your oil painting is the environment: dust, air pollution, UV rays, smoke, pet hair, kids with crayons, red wine splashes. The list is endless. Canvas is porous and if left open to room air, it actually acts like a filter for that air, absorbing chemical and particulate pollution.

Advice from the British Conservation Register on cleaning without glass:


  Dust can be removed using a very soft brush with metal elements protected so that they cannot be a cause of damage. Avoid feather dusters, sheep skin dusters, however soft, as they catch. You must be careful to check that there is no paint flaking before dusting. Do not attempt any dusting if the surface appears unstable.


Below is an example of flaking:



Further examples of flaking can be found on the Painting Conservation Studio website, from where the above image came.

It is much easier to clean the glass or acrylic than to pay for an expert conservator to restore your painting.

If you choose to keep the glass, make sure that the glass is spaced so it does not touch the artwork. A professional picture framer can advise you in this regard, as well as recommend a quality UV protecting glass that will preserve the clarity of the painting.

Further advice from the British Conservation Register on cleaning the glass:


  Always spray glass cleaner onto the cloth, not the glass. Spray well away from your painting. The use of backboards is recommended as a preventive conservation measure to protect against the accumulation of dust and dirt, as well as against knocks and accidental damage. A conservator can fit backboards to your paintings for you.


When deciding what to do, ask yourself these questions:


Does this canvas artwork hold great sentimental value to me?
Am I keeping the artwork to enjoy for a long time?
Will I eventually want to resell the artwork?


If the answer is yes to any of these questions, and the work is older than 1 year, then keeping glass will probably be a good long term choice.