You don't mention any details regarding the grout being used, but my first thought is that the chalky limestone is able to absorb enough water from the grout so that the grout quickly "cakes" up the fractures around the borehole and seals them from receiving any further grout.  Are you using bentonite in your grout?

Grout-ability is mainly governed by PSD (Particle Size Distribution) of the grout powder. 

Normal cement has maximum particle size (d95) of 80 microns. This will not be able to penetrate in finest of the pores strata like the one you have; inspite of increaeing the pressure.

You can try with blended ultra-fine cement grouts with d95 < 12 microns which are specifically made for permeation grouting under the dam structure. 

Hi. You must differentiate between CRACKs and POREs. For rocks the main target is the cracks. But in both cases the Groutability Ratio is governing issue. We have no information on the crack characterstics. I see from the pictures that you are dealing with cavities which form due to dissoultioning of lime. (please be very careful. You may be dealing with Karstification). Chemical Grouting consisted of materials which dissolve in water may be a solution. But they are expensive. You must decide based on your local situation. Regards

It seems you are faced with karstified limestone and there beside the grout mixture, the applied presssure also the drilling distance is very important.

kind regards

Chalk is a fine grained rock. If the joints are filled with fine grained clay, it is difficult for the grout mass with ordinary cement to penetrate. If the W/C ratio is less than 1 it will be even difficult. Micro-cement is an alternative, however for mass grouting it may become very expensive. Use 5 to 10 percent bentonite and and W/C ration of about 1.5 to 2, you may achieve different result. Good luck!