Is the value of `this` pointer constant during the object's lifetime?

Is the value of this pointer guaranteed to be constant during a lifetime of a particular object?

Yes.

As user Aconcagua puts it: the value of this pointer always is the value of the address of the object on which the function was called on¹. So the question is equivalent with:

Can an object change its memory address over life time?

This is not possible, by definition of lifetime². The lifetime of an object begins when or after its storage is obtained and ends before of when it is released.

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¹⁾ [class.this]/1

In the body of a non-static ([class.mfct]) member function, the keyword this is a prvalue whose value is a pointer to the object for which the function is called.

²⁾ [basic.life]/1 (emphasis mine)

The lifetime of an object or reference is a runtime property of the object or reference. A variable is said to have vacuous initialization if it is default-initialized and, if it is of class type or a (possibly multi-dimensional) array thereof, that class type has a trivial default constructor. The lifetime of an object of type T begins when:

• storage with the proper alignment and size for type T is obtained, and
• its initialization (if any) is complete (including vacuous initialization) ([dcl.init]), except that if the object is a union member or subobject thereof, its lifetime only begins if that union member is the initialized member in the union ([dcl.init.aggr], [class.base.init]), or as described in [class.union].

The lifetime of an object o of type T ends when:

• if T is a non-class type, the object is destroyed, or
• if T is a class type, the destructor call starts, or
• the storage which the object occupies is released, or is reused by an object that is not nested within o ([intro.object]).

An object has a region of storage. this points there.

[intro.object]/1

An object occupies a region of storage in its period of construction ([class.cdtor]), throughout its lifetime, and in its period of destruction ([class.cdtor]).