I'd check you have sufficient water in the system, as Ian has suggested, before condemning the pump. If need be, drain some off and see if the system refills.
If the pilot light goes out when the main burner turns off I would suspect the gas valve. I have a boiler of similar age and parentage and the only time I've had the pilot light go out unintentionally was during a violent storm with exceptionally high winds.I have noticed this evening that each time it shuts down, after 10-15 mins, the pilot light is going out and I have to re light it.
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