Is it possible to manufacture Helium? Helium is a scarce resource, as it escapes the atmosphere over time. If we run out of Helium deposits, will it be possible to manufacture more helium through nuclear fusion or another nuclear process? If so, how much energy will be required?
 A: Helium is a non-renewable natural resource.
The helium that is available commercially is extracted from oil and gas wells.  Helium can be extracted from underground because it is trapped by the same sorts of impermeable rock layers that trap petrochemicals.  That helium has had thousands or millions of years to accumulate in those rock formations, but we can empty them in a few decades.  We are removing helium from shallow underground deposits at a much faster rate than it's being replaced by deep underground radioactivity; the equilibrium is broken.
It is possible to generate $\alpha$ particles in accelerator reactions, and an $\alpha$ will eventually slow down, steal two electrons, and act like helium.  But generating chemically significant quantities of nuclear decay products takes an unrealistic energy commitment.  Typically to remove a particle from a nucleus involves a reaction energy of 2–10 MeV.  At one point for a homework assignment I learned that a Hiroshima-type fission explosion produces roughly 1 kg of free neutrons; in the same assignment I figured that a new accelerator neutron source would produce roughly 1 kg of free neutrons over its expected 30 year operating life.
The accelerator neutron source gives you an idea of the scale that'd be required for industrial-scale helium manufacture.  It'd take a billion-dollar capital investment to build the facility, hundreds of millions per year in operating costs, and with good engineering and good luck the helium output might be measured in kilograms per year.  You wouldn't use that for balloons any more.

Blackbody Blacklight proposes in a comment to extract the alpha particles from nuclear waste.  Suppose you have 4000 moles of plutonium, with mass 4 × 240 kg (that is, about a ton), decay half-life of 104 years, and a hypothetical fast decay chain that makes ten alpha particles.  You extract all the alpha particles as helium.  After 104 years you have a half-ton of plutonium, a half-ton of lead, and 20 kmol of helium, with mass 80 kg.  So a ton of highly-active, alpha-emitting waste gives off helium at a rate of ten or twenty grams per year.  For a real reactor, this ton of plutonium would be spread across about 100 total tons of waste.  This is more economical than the accelerator option, but not economical enough that it will ever see much use.
A: It is somewhat misleading to refer to the depletion of "helium deposits".
Helium is being produced constantly as alpha particles in nuclear decay throughout the mass of the earth.  The principle sources are naturally occurring uranium and thorium and their decay products.  This helium then transits through the earth and may collect in natural gas deposits. It then passes through the atmosphere and into space.
We temporarily use some of this helium as it passes through...
So, helium is already being naturally manufactured, and for free... 
