MKR GPS Shield library only works if you call GPS.Available() non-stop

Look at the example code for your device using the library:

/*
  GPS Location
  This sketch uses the GPS to determine the location of the board
  and prints it to the Serial Monitor.
  Circuit:
   - MKR board
   - MKR GPS Shield attached via I2C cable
  This example code is in the public domain.
*/

#include <Arduino_MKRGPS.h>

void setup() {
  // initialize serial communications and wait for port to open:
  Serial.begin(9600);
  while (!Serial) {
    ; // wait for serial port to connect. Needed for native USB port only
  }

  // If you are using the MKR GPS as shield, change the next line to pass
  // the GPS_MODE_SHIELD parameter to the GPS.begin(...)
  if (!GPS.begin()) {
    Serial.println("Failed to initialize GPS!");
    while (1);
  }
}

void loop() {
  // check if there is new GPS data available
  if (GPS.available()) {
    // read GPS values
    float latitude   = GPS.latitude();
    float longitude  = GPS.longitude();
    float altitude   = GPS.altitude();
    float speed      = GPS.speed();
    int   satellites = GPS.satellites();

    // print GPS values
    Serial.print("Location: ");
    Serial.print(latitude, 7);
    Serial.print(", ");
    Serial.println(longitude, 7);

    Serial.print("Altitude: ");
    Serial.print(altitude);
    Serial.println("m");

    Serial.print("Ground speed: ");
    Serial.print(speed);
    Serial.println(" km/h");

    Serial.print("Number of satellites: ");
    Serial.println(satellites);

    Serial.println();
  }
}

GPS.available() just means if the GPS has data available do the thing. It's all good and you do not have an issue.