Is bachelor degree after master degree in the same subject valid?

Though it is not essential to have passed graduation along with the subject of Philosophy for undertaking post graduation in the same subject. Your graduation degree of BE in Mechanical Engineering is enough for taking up M.A. in Philosophy and certainly you were permitted to write your papers in M.A. in Philosophy even though you did not have a degree along with the same subject at your degree stage.
However, please note that all the universities don't follow strictly that at the graduation stage one should pass with the same subject in which one is to pursue his post graduation.
You will have to make an enquiry from the other universities as well to know the real position.
Some universities such as JNU, BHU, Aligarh Muslim University permit aspirants to write their M.A in Philosophy irrespective of selection of any stream in the graduation levels. They conduct oral tests for the scrutiny of aspirants so as to assess their potentials for undertaking post graduation in the subjects they are interested to pursue.
Hence you have to verify the eligibility conditions from the other quarters as well.

You did you BE Mechanical and then you did your MA in Philosophy. But your application for an Assistant professor post was rejected as you have not done your graduation in Philosophy,
You can do your graduation in Philosophy after doing PG also from another university. There is no objection to that. The same university may not allow you to do that but other universities will not have any objection. Even you can think of doing a BA through correspondence school or open university. You can go to the site of IGNOU and see the course content and select subjects that suit you and one of them can be philosophy. There are many other universities offering this course through distance mode.

As mentioned above, you did your M.A in philosophy after completing BE in mechanical engineering. But, now you want to do graduation in philosophy because your application got rejected for assistant professor. You can do graduation in philosophy. There would not be any problem. There are many universities in India which offer this course on a regular basis. You can apply for that. Besides, you can do this course through distance mode also like IGNOU annamalai university etc. The same University may object to your joining degree course but another university would allow it easily.

It is obvious that your bachelor degree is professional/technical, but your post graduation is arts group, so relevance created confusion in the minds of selector. Instead you would have done PG in technology or you would have not mentioned your PG as you might have done your PG on your interest.

Many universities allow students to take up their PG in some of the subjects though they had not done their UG in those particular subjects. Due to this facility many people do their PG the way you have done it. Your case appears as a rare one because doing a PG in Philosophy after engineering stream is not so common a thing.
In my opinion and view there is absolutely no problem in this case as you can go for a UG degree in some subjects including Philosophy. That would eat up a few years in your career but that only seems a possible option at the present juncture.
Career making is a tricky thing and sometimes we end up losing our precious young years in that. Teaching is a good profession and the career starting with Assistant Professor is a lucrative proposition but there are many other options also. There are many competitive exams like civil services, state services, banking services, subordinate services etc where your acquired knowledge can be put to use and you can think of making a career accordingly.
Being an engineer have you ever considered starting your own work in self employment mode? I am just giving these ideas to you to look upon other alternatives instead of wasting few more years for a UG degree.