A “fixed” semicont variable has still the implicit lower bound of 0. In order to truly fix it the variable needs to be relaxed via RMIP or to add to attribute prior=INF. The example below illustrates this.

variable x,z;
semicont variable x;
equation e;
e.. z =e= x;
model m /all/;

* A "fixed" semicont variable has still the implicit lower bound of 0
* The domain for x is {0,1}
x.fx=1; solve m us mip min z; abort$(abs(z.l-0)>1e-6) 'wrong obj';

* In order to truly fix it the variable needs to be relaxed via RMIP or prior=INF
* Solved as an RMIP the domain of x becomes {1}
x.fx=1; solve m us rmip min z; abort$(abs(z.l-1)>1e-6) 'wrong obj';

* Solved as a MIP with x.prior=INF the domain of x becomes also {1}
x.fx=1; x.prior=INF; solve m us mip min z; abort$(abs(z.l-1)>1e-6) 'wrong obj';

* Since x is not truly fixed (domain is {0,1}) holdfixed does not "hold" x
x.fx=1; m.holdfixed=1; solve m us mip min z; abort$(m.numvar<>2) 'x hold incorrectly';

* Holdfixed does not "hold" semicont variables even if they are relaxed and truely fixed
x.fx=1; m.holdfixed=1; solve m us rmip min z; abort$(m.numvar<>2) 'x hold incorrectly';

* Holdfixed does not "hold" semicont variables even if they are relaxed and truly fixed
x.fx=1; x.prior=INF; m.holdfixed=1; solve m us mip min z; abort$(m.numvar<>2) 'x hold incorrectly';