Yes, an isolated brain SHOULD have a substantially extended lifespan, with a few caveats.
For starters, removing the biological body should eliminate many other reasons for premature death (infection, trauma, organ failure, cancer) which will boost the average life expectancy. This assumes the synthetic body is at least as effective as our biological ones and allows for easy replacement of worn parts. The brain case may also be much better at protecting the brain, preventing microtrauma and coup-contrecoup injury from impacts. Cerebrospinal fluid (well, maybe just cerebral fluid now) would be full all the time, so no dehydration related increase in brain injury.
Second, isolating the brain should allow for a "perfect" diet for maintenance of non-neural support structures (preventing cholesterol plaque buildup in the blood vessels, appropriate nutrients with omega-3 fatty acids, etc) which will optimize the potential of the organic tissue. This assumes a thorough understanding of the nutrient requirements of the tissue and an ability to supply these organic and non-organic nutrients. Doping the brain with telomerase and other substances (at this level of tech, probably tailored viruses and nanomachines) to prevent/repair genetic damage, telomere depletion, and terminal blood vessel injury would prevent accumulation of eventually fatal damage to the brain and support structure.
Third, toxic substances/scenarios should be limited. Alcohol, for example, may not be a concern for an isolated brain. Fluctuations in blood pressure should be limited, both elevated pressure which could rupture blood vessels and cause strokes and drops in pressure which would lead to hypoxia. It may also be possible to inject protective compounds when necessary (for example, THC has been shown to be very protective in reducing traumatic brain injury following impact). Preventing heavy metal toxicity may reduce some debilitating neural diseases (some linkage to Alzheimer's) and prevention of infection may also help.
Presumably isolation from the body would cause SOME problems though. There is literature to suggest that some neurotransmitters are actually manufactured by the GI tract, so that would have to be replicated. Even if synthetic blood can replicate O2/CO2 exchange and waste removal, the immune system and some sort of bone marrow analogue would be necessary. A stockpile or means of generating pluripotent stem cells would also be necessary, as we learn more about the brain it does not appear to be as static as we once thought. There are also feedback mechanisms that reply on organs south of the brain, these would have to be artificially regulated. There are also protective neurologic reflexes and sympathetic/parasympathetic feedback systems that would have to be replicated in a synthetic body lest the isolated brain fail to respond appropriately to damaging external stimuli.
Psychologically of course eliminating the biological body carries an enormous risk. We rely heavily on feedback from our body to develop our psyche and conduct the "normal business" of living. For example, folks with a feeding tube who no longer need to eat report a significant drop in quality of life because the dopamine reward system associated with physically tasting and chewing food is now absent. I suspect, much like the examples provided by Robocop 2, it would require a special psyche to be able to adapt to a synthetic body unless it PERFECTLY recreates the experience of being human. Otherwise supplanting the body's reward mechanisms with drugs would probably be pretty common.
EDIT: I'll mention some other considerations that tangentially at least will affect brain lifespan. Currently at least, interfacing biologic systems with synthetic ones is very problematic. Even something like a prosthetic limb causes irritation where it joins the body. For an isolated brain nerve endings would have to mate with synthetic components, both for sensory input and for motor action. Now there is some possibility that you could induce sensory input/derive motor output remotely by magnetically reading the brain and stimulating certain areas but this would probably be VERY low bandwidth for quite some time. So instead you have to hook up cranial nerves (there are twelve pairs of them) to sensors, at least the important ones for vision, smell, taste, etc. So a biological nerve interfacing with a synthetic sensor, even if it doesn't directly connect (instead using some sort of neurotransmitter gap) will typically stimulate an inflammatory reaction. This can be downregulated with corticosteroids/immunosuppressants, and indeed without a body and bone marrow the isolated brain may have NO INTRINSIC IMMUNE SYSTEM, thus it would be very vulnerable to any introduced microorganism, so it's nutrient supply and components would have to be rigorously sterilized and the cerebral fluid would need constant monitoring so anti-microbial anti-biotics/nanites could be introduced. But an immune system also helps destroy emerging cancer cells, so there would have to be a system to perform that task as well. Now it is possible that your synthetic body is in fact at least partly organic itself (i.e., built using carbohydrates, lipids, and proteins, utilizing chemical gradients and biochemical processes rather than mechanical ones) which may reduce the inherent difficulty in getting organic tissue to work well with mechanical parts (I'll just assume that graft vs host rejection has been resolved at this tech level). You also have to consider how you would map the severed spinal cord trunk to whatever interface conducts motor neuron impulses to the synthetic body (as it seems like you intend for this brain to have a humanoid robot body). This process is difficult to mass produce because currently our brains "learn" which neurons do what as we grow and the spinal cord wiring isn't necessarily the same from person to person. But it ought to be roughly similar enough that a new brain/body would have some level of control, but they would have to go through some intensive physical therapy while their brains rewires itself to accommodate the way the new body functions. This spinal cord interface would also have the same organic/machine interface problems as sensory nerves.
Anyway, very long winded way to say that the complexities of the brain/machine interface itself could lead to degradation, inflammation, and serve as a nidus of infection. Constant low level inflammation is associated with increased incidence of cancer. So it is quite possible that an entire new set of diseases crops up around these hybrid organisms, which may negatively impact their lifespan.