Why mass spectra of 2-methylbutane do not show big peak at 71 coming from tertiary carbocation? Mass spectra of 2-methylbutane show strong peak at 57 by loss of methyl radical to give secondary carbocation while a loss of hydrogen radical from 2-position would form tertiary carbocation with m/z = 71 peak.

Since rules suggest that it is the stability of carbocation that determines the fragmentation pattern.So this process must be more favorable process still we do not get base peak at 71 instead we get a small peak at 71.

Same pattern is observed in case of 2-methylpentane where M-1 peak is almost absent. Other compounds also do not favor loss of hydrogen radicals to give M-1 peak.

I had read about this somewhere that it had something to do with energy of overall process but not able to recall. Kindly help me to explain the reason behind this phenomenon.
How do you know that losing a CH3 radical gives you a secondary carbocation?
Maybe it will perform a hydride shift and you land at the tertiary carbocation.
Always take this into account, because you can shoot yourself in the foot if you assume carbocations to be too stable. In EI, they rearrange all the time (e.g. benzylium &lt;-> tropylium).
However, seeing that the ion with $m/z~57$ subsequently looses $\mathrm{\text{:}CH_2}$, it seems reasonable to assume that the secondary carbocation is formed here.

The important point is the following: You propose that instead of loosing the methylradical, yielding a secondary carbocation (or a tertiary, considering the argument from above), there should be a loss of a hydrogen radical. 
However, the hydrogen radical is far less stable than the methyl radical, and I assume this is the reason for the regioselectivity, here.

Also keep in mind that you supply a lot of energy (70 eV). Hence, the induced fragmentation processes are highly endothermic, and should be under kinetic control.

If you really want to find out what is going on, you should probably have a look at McLafferty's/Turecek's classic textbook "Interpretation of Mass Spectra".