Magnetic flux in the solar photosphere forms concentrations from small scales, such as flux elements, to large scales, such as sunspots. This paper presents a study of the decay process of large magnetic flux tubes, such as sunspots, on a supergranular scale. Three-dimensional nonlinear resistive magnetohydrodynamic numerical simulations are performed in a cylindrical domain, initialized with axisymmetric solutions that consist of a well-defined central flux tube and an annular convection cell surrounding it. As the nonlinear convection evolves, the annular cell breaks up into many cells in the azimuthal direction, allowing magnetic flux to slip between cells away from the central flux tube (turbulent erosion). This lowers magnetic pressure in the central tube, and convection grows inside the tube, possibly becoming strong enough to push the tube apart. A remnant of the central flux tube persists with nonsymmetric perturbations caused by the convection surrounding it. Secondary flux concentrations form between convection cells away from the central tube. Tube decay is dependent on the convection around the tube. Convection cells forming inside the tube as time-dependent outflows will remove magnetic flux. (This is most pronounced for small tubes.) Flux is added to the tube when flux caught in the surrounding convection is pushed toward it. The tube persists when convection inside the tube is sufficiently suppressed by the remaining magnetic field. All examples of persistent tubes have the same effective magnetic field strength, consistent with the observation that pores and sunspot umbrae all have roughly the same magnetic field strength.