differential equations – FindRoot::dfmin: The minimal damping factor of 1/10000 has been reached

I have to solve a highly nonlinear parametric system of three PDEs.
I don’t know to which extent the results are trustable. Indeed, the graph shown
by ParametricNDSolve also presents the error message “FindRoot::dfmin: The minimal damping factor of 1/10000 has been reached”. Here is the code.
Any help to fix this code is greatly welcome. Thanks.

(* fixed parameters *)
fixed = {Rext -> 1.5, DeltaP -> 1, pin -> 1, ps -> -0.62, Os -> 0.37, 
G2 -> 0.53, G3 -> 0.21, cs -> 0.5, phiiniz -> 0.4, c0 -> 0.07, 
c1 -> 2.49, c2 -> 1107, c3 -> 1.69, theta -> 310};

(*some auxiliary functions *)
f(xi_, alpha_) := 1/(1 + alpha* xi)
gamma(H_) := -1 + (1 - 
 H (c0 Exp(c1 H + c2 theta^(-1) Exp(-c3 H))))^(-1)
CapGamma(x_) := x + G2 x^2 + G3 x^3
press(x_) := (pin - ps) - DeltaP *x

(*variable parameters *)
params = {alpha, G, A, T};

(* parametric system of pdes *)
eqns = {D(phi(x, t), x) == 
 16 G *f(xi(x, t), alpha) (DeltaP *Log(Rext))^(-1) ( 
   press(x) - 
    Os (CapGamma(c(x, t) (1 - phi(x, t))^(-1)) - CapGamma(cs)))*
  phi(x, t) (1 + gamma(phi(x, t))), phi(0, t) == phiiniz, 
D(c(x, t), x) == 
 16 G * f(xi(x, t), phi(x, t)) (DeltaP *Log(Rext))^(-1) ( 
   press(x) - 
    Os (CapGamma(c(x, t) (1 - phi(x, t))^(-1)) - CapGamma(cs)))*
  c(x, t) (1 + gamma(phi(x, t))), c(0, t) == 1, 
D(xi(x, t), t) == 
 G *f(xi(x, t), phi(x, t)) (DeltaP *Log(Rext))^(-1) ( 
    press(x) - 
     Os (CapGamma(c(x, t) (1 - phi(x, t))^(-1)) - CapGamma(cs)))*
   c(x, t) - 0.5*A*DeltaP*xi(x, t), xi(x, 0) == 0} /. fixed;

(*solving *)
 sol = ParametricNDSolve(eqns, {phi, c, xi}, {x, 0, 1}, {t, 0, T}, 
 params, MaxSteps -> Infinity);

(*visualization *)
 Manipulate(
 Plot3D(Evaluate(xi(phi, G, A, T)(x, t) /. sol), {x, 0, 1}, {t, 0, T},
 Axes -> True, AxesLabel -> {x, t, xi}, AxesStyle -> Directive(16), 
Mesh -> False, PlotRange -> {Full, Full, All}), {phi, 1, 10}, {G, 1,
20}, {A, 1, 20}, {T, 1, 10})

 (!(solution)(1))(1)
 FindRoot::dfmin: The minimal damping factor of 1/10000 has been reached.

 (1): https://i.stack.imgur.com/N0twi.png