  We study the frog model with death on the biregular tree
$\mathbb{T}_{d_1,d_2}$. Initially, there is a random number of awake and
sleeping particles located on the vertices of the tree. Each awake particle
moves as a discrete-time independent simple random walk on
$\mathbb{T}_{d_1,d_2}$ and has a probability of death $(1-p)$ before each step.
When an awake particle visits a vertex which has not been visited previously,
the sleeping particles placed there are awakened. We prove that this model
undergoes a phase transition: for values of $p$ below a critical probability
$p_c$, the system dies out almost surely, and for $p > p_c$, the system
survives with positive probability. We establish explicit bounds for $p_c$ in
the case of random initial configuration. For the model starting with one
particle per vertex, the critical probability satisfies
$p_c(\mathbb{T}_{d_1,d_2}) = 1/2 + \Theta(1/d_1+1/d_2)$ as $d_1, d_2 \to
\infty$.
