Should a disability pension still continue even after age 65 when the disability is still there?

Saying the Word "should" insinuates an opinion based question. There is an opinion portion to this, but more importantly is the factual portion.

If I understand this question correctly, it is asking whether or not Disability benefits will pay out beyond age 65. The answer is that in some cases it will and and in some cases it will not.

It will pay beyond age 65 if:
You are disabled and receiving benefits from an individual Disability insurance policy that has a maximum benefit period of age 67 or 70. Additionally, some contracts will have provisions stating that if you become disabled at any age later than 60, the policy will pay benefits for a limited or specific number of years. You can check the guidelines of your contract to see the circumstances in which benefits would be paid after age 65.
If you are disabled and receiving Social Security you may be eligible to receive benefits beyond age 65 as well. This will be dependent on your birth year.

It will not pay beyond age 65 if:
You are disabled and receiving benefits from an individual or group Disability insurance policy that has a maximum benefit period of to age 65.

Regarding Social Security disability benefits, when they terminate at retirement age, the benefits will change from disability to retirement benefits. The primary concern at this point is how much your retirement benefits will be if you have been disabled and out of the work force for an extensive period of time.