Is it possible for a baptized saved Christian to lose the Holy Spirit after receiving it like in Saul’s case who was disobedient and it was taken away from him?
Yes, it definitely is possible for a baptized/saved Christian to lose the gift of the Holy Spirit. I do not believe what happened to Saul in 1 Samuel is a very good example. I say this because as far as we know biblically, Saul did not have the indwelling gift of the Holy Spirit. The promised gift of the Holy Spirit is given only to those who are, after repenting, baptized into Christ (Acts 2:26-41).
There is at the web site a good amount of material on this question. I suggest you go to the "store" and find an audio titled "Hebrews, Fate or Freedom." There is also a power point and set of notes on the same subject in the power point section of the site.
Let me give you a very brief synapsis, explaining why I am quite convinced that it is possible for us to lose our salvation and for the Holy Spirit to leave us. Many scriptures to this effect can be given, but let me go to the book of Hebrews. First there is Hebrews 3:12-4:11 which is a stern warning to us to not turn back, not fail to listen, to instead make every effort to enter the spiritual "Promised Land," which is in heaven with God. The writer of Hebrews admonishes us that we can lose our salvation. Leaving Egypt (ie being saved) is not a guarantee of making it to the Promised Land (heaven).
Then there is Hebrews 6:4-12. Here, those who have been saved are given the most stern possible warning against turning back and losing our salvation. The writer of Hebrews tells us that "It is impossible for those who have once been enlightened (a code word in the early church for those who have been baptized), who have tasted the heavenly gift, who have shared in the Holy Spirit… if they fall away, to be brought back to repentance, because to their loss they are crucifying the Son of God all over again and subjecting him to public disgrace. Here there is no question at all that he is talking about those who have been baptized and received the Holy Spirit. In 6:12 he concludes that his goal is for us to make our salvation sure. We must be diligent to the end in order to be (ultimately) saved. This is a clear statement that we can forfeit the promised salvation and the Holy Spirit if we do not stay diligent to the end.
Last of all, there is Hebrews 10:26-31 which is perhaps the sternest warning in the New Testament. The Hebrew writer tells us that if we continue in deliberate sin, "no sacrifice for sins is left, but only a fearful expectation of judgment and of raging fire that will consume the enemies of God." He says that those who willfully return to a life of sin "trample the Son of God underfoot" and "insult the Spirit of grace." There is no doubt that at some point the Holy Spirit will leave us. Like Peter warned us, if we leave the corruption of the world, but are again entangled in it we are worse off than we were at first (2 Peter 2:20-21). This is true because if we return to the world, we will lose the gift of the Holy Spirit. Biblically, this is irreversible.
May this never happen to you!