diff --git a/onnxruntime/core/framework/bfc_arena.cc b/onnxruntime/core/framework/bfc_arena.cc
index 71c2e09773..ec7fca5c82 100644
--- a/onnxruntime/core/framework/bfc_arena.cc
+++ b/onnxruntime/core/framework/bfc_arena.cc
@@ -144,7 +144,14 @@ Status BFCArena::Extend(size_t rounded_bytes) {
   // Try allocating less memory.
   while (mem_addr == nullptr) {
     bytes = RoundedBytes(static_cast<size_t>(bytes * kBackpedalFactor));
-    if (bytes < rounded_bytes)
+
+    // give up if we can't satisfy the requested size, or we're attempting an allocation of less than 8K.
+    //
+    // the latter protects against an infinite loop that occurs when bytes is less than 2560. at that point the 10%
+    // reduction to 2304 bytes is undone by rounding to a 256 boundary in RoundedBytes, leading to an infinite loop.
+    // the 8K value is just to give up a little earlier vs. getting all the way down to 2560 bytes.
+    // If we can't allocate 8K, we're pretty much dead.
+    if (bytes < rounded_bytes || bytes < 8 * 1024)
       break;
 
     mem_addr = safe_alloc(bytes);
diff --git a/onnxruntime/test/framework/bfc_arena_test.cc b/onnxruntime/test/framework/bfc_arena_test.cc
index df265922cb..873032fa37 100644
--- a/onnxruntime/test/framework/bfc_arena_test.cc
+++ b/onnxruntime/test/framework/bfc_arena_test.cc
@@ -284,5 +284,19 @@ TEST(BFCArenaTest, TestReserve) {
   a.GetStats(&stats);
   EXPECT_EQ(stats.total_allocated_bytes, 1048576);
 }
+
+class BadAllocator : public IAllocator {
+ public:
+  BadAllocator() : IAllocator(OrtMemoryInfo(CPU, OrtAllocatorType::OrtDeviceAllocator)) {}
+
+  void* Alloc(size_t /*size*/) override { throw std::bad_alloc(); }
+  void Free(void* /*p*/) override {}
+};
+
+TEST(BFCArenaTest, TestBackoffDoesntHang) {
+  // test that if there are allocation failures the backoff logic doesn't hang. See comments in BFCArena::Extend
+  BFCArena a(std::unique_ptr<IAllocator>(new BadAllocator()), 10 * 1024 * 1024);
+  EXPECT_THROW(a.Alloc(1024), OnnxRuntimeException) << "Arena should be unable to allocate memory";
+}
 }  // namespace test
 }  // namespace onnxruntime