diff --git a/diffrax/_integrate.py b/diffrax/_integrate.py
index 8241fa9b..5441e0a9 100644
--- a/diffrax/_integrate.py
+++ b/diffrax/_integrate.py
@@ -275,13 +275,13 @@ def _save(
     )
 
 
-def _clip_to_end(tprev, tnext, t1, t1_clip_floor, keep_step):
+def _clip_to_end(tnext, t1, t1_clip_floor, keep_step):
     # The tolerance of ~100 ULP's means that we don't end up with too-small intervals
     # for dense output, which then gives numerically unstable answers due to floating
     # point errors.
-    clip = tnext > t1_clip_floor
-    tclip = jnp.where(keep_step, t1, tprev + 0.5 * (t1 - tprev))
-    return jnp.where(clip, tclip, tnext)
+    # Only clip on accepted steps: on a rejection the controller has just shrunk its
+    # proposal, so overriding it can cause an infinite rejection loop (see #756).
+    return jnp.where(keep_step & (tnext > t1_clip_floor), t1, tnext)
 
 
 def _maybe_static(static_x: ArrayLike | None, x: ArrayLike) -> ArrayLike:
@@ -410,7 +410,7 @@ def body_fun_aux(state):
         #
 
         tprev = jnp.minimum(tprev, t1)
-        tnext = _clip_to_end(tprev, tnext, t1, t1_clip_floor, keep_step)
+        tnext = _clip_to_end(tnext, t1, t1_clip_floor, keep_step)
 
         progress_meter_state = progress_meter.step(
             state.progress_meter_state, linear_rescale(t0, tprev, t1)
diff --git a/test/test_adaptive_stepsize_controller.py b/test/test_adaptive_stepsize_controller.py
index d785d16e..4a51336f 100644
--- a/test/test_adaptive_stepsize_controller.py
+++ b/test/test_adaptive_stepsize_controller.py
@@ -364,6 +364,64 @@ def test_jump_at_t1_with_large_t1_in_float32():
     assert sol.ts == jnp.array([t1])
 
 
+# https://github.com/patrick-kidger/diffrax/issues/756
+# In float32 with a large t1, the 100-ULP clip window is wide enough to contain
+# the PID controller's desired step. If tprev sits just outside the clip window
+# but the controller's proposed tnext is inside it, the rejected step must not
+# be overridden with a fixed midpoint between tprev and t1: tprev does not move
+# on rejection, so a fixed midpoint would be retried forever.
+def test_clip_to_end_does_not_override_rejected_step():
+    from diffrax._integrate import _clip_to_end
+
+    t1 = jnp.array(600.0, dtype=jnp.float32)
+    t1_clip_floor = t1
+    for _ in range(100):
+        t1_clip_floor = eqxi.prevbefore(t1_clip_floor)
+    # tnext lies inside the clip window; the controller has just rejected the
+    # previous step, so keep_step is False. Expect the controller's tnext to
+    # pass through unchanged (so the next iteration sees a strictly shrunken
+    # proposal rather than the same midpoint).
+    tnext = jnp.array(599.996, dtype=jnp.float32)
+    assert tnext > t1_clip_floor
+    out = _clip_to_end(tnext, t1, t1_clip_floor, jnp.array(False))
+    assert out == tnext
+    # On an accepted step we still snap to t1.
+    out = _clip_to_end(tnext, t1, t1_clip_floor, jnp.array(True))
+    assert out == t1
+    # And outside the clip window we never touch tnext.
+    tnext_far = jnp.array(599.0, dtype=jnp.float32)
+    for keep in (jnp.array(True), jnp.array(False)):
+        assert _clip_to_end(tnext_far, t1, t1_clip_floor, keep) == tnext_far
+
+
+# End-to-end version of the above: a harmonic oscillator in float32 with t1=600
+# and a tolerance that drives the PID controller's desired step into the 100-ULP
+# clip window. Before the #756 fix this hung at max_steps with tprev pinned to
+# the clip floor; after the fix it completes in ~30 steps.
+def test_no_infinite_reject_loop_at_t1_in_float32():
+    t1 = jnp.float32(600.0)
+    omega = jnp.float32(1000.0)
+
+    def vf(t, y, args):
+        y0, y1 = y
+        return jnp.stack([y1, -omega * omega * y0])
+
+    sol = diffrax.diffeqsolve(
+        diffrax.ODETerm(vf),
+        diffrax.Tsit5(),
+        t0=jnp.float32(599.99),
+        t1=t1,
+        dt0=None,
+        y0=jnp.array([1.0, 0.0], dtype=jnp.float32),
+        stepsize_controller=diffrax.PIDController(rtol=1e-4, atol=1e-4, safety=0.9),
+        saveat=diffrax.SaveAt(t1=True),
+        max_steps=1000,
+    )
+    assert sol.result == diffrax.RESULTS.successful
+    assert sol.ts is not None
+    assert sol.ts[-1] == t1
+
+
 # https://github.com/patrick-kidger/diffrax/issues/713
 def test_t0_at_jump_time():
     jump_time = 0.98