diff --git a/flang/runtime/connection.h b/flang/runtime/connection.h
--- a/flang/runtime/connection.h
+++ b/flang/runtime/connection.h
@@ -57,6 +57,12 @@
   // or an end-of-file READ condition on a sequential access file
   std::optional<std::int64_t> endfileRecordNumber;
 
+  // Set when processing repeated items during list-directed & NAMELIST input
+  // in order to keep a span of records in frame on a non-positionable file,
+  // so that backspacing to the beginning of the repeated item doesn't require
+  // repositioning the external storage medium when that's impossible.
+  std::optional<std::int64_t> resumptionRecordNumber;
+
   // Mutable modes set at OPEN() that can be overridden in READ/WRITE & FORMAT
   MutableModes modes; // BLANK=, DECIMAL=, SIGN=, ROUND=, PAD=, DELIM=, kP
 };
diff --git a/flang/runtime/io-stmt.h b/flang/runtime/io-stmt.h
--- a/flang/runtime/io-stmt.h
+++ b/flang/runtime/io-stmt.h
@@ -229,7 +229,6 @@
 
 private:
   int remaining_{0}; // for "r*" repetition
-  std::int64_t repeatRecordNumber_;
   std::int64_t repeatPositionInRecord_;
   bool eatComma_{false}; // consume comma after previously read item
   bool hitSlash_{false}; // once '/' is seen, nullify further items
diff --git a/flang/runtime/io-stmt.cpp b/flang/runtime/io-stmt.cpp
--- a/flang/runtime/io-stmt.cpp
+++ b/flang/runtime/io-stmt.cpp
@@ -653,7 +653,11 @@
     comma = ';';
   }
   if (remaining_ > 0 && !realPart_) { // "r*c" repetition in progress
-    while (connection.currentRecordNumber > repeatRecordNumber_) {
+    RUNTIME_CHECK(
+        io.GetIoErrorHandler(), connection.resumptionRecordNumber.has_value());
+    while (connection.currentRecordNumber >
+        connection.resumptionRecordNumber.value_or(
+            connection.currentRecordNumber)) {
       io.BackspaceRecord();
     }
     connection.HandleAbsolutePosition(repeatPositionInRecord_);
@@ -666,6 +670,9 @@
       }
     }
     remaining_ -= edit.repeat;
+    if (remaining_ <= 0) {
+      connection.resumptionRecordNumber.reset();
+    }
     return edit;
   }
   // Skip separators, handle a "r*c" repeat count; see 13.10.2 in Fortran 2018
@@ -726,7 +733,11 @@
       }
       edit.repeat = std::min<int>(r, maxRepeat);
       remaining_ = r - edit.repeat;
-      repeatRecordNumber_ = connection.currentRecordNumber;
+      if (remaining_ > 0) {
+        connection.resumptionRecordNumber = connection.currentRecordNumber;
+      } else {
+        connection.resumptionRecordNumber.reset();
+      }
       repeatPositionInRecord_ = connection.positionInRecord;
     } else { // not a repetition count, just an integer value; rewind
       connection.positionInRecord = start;
diff --git a/flang/runtime/unit.cpp b/flang/runtime/unit.cpp
--- a/flang/runtime/unit.cpp
+++ b/flang/runtime/unit.cpp
@@ -350,13 +350,10 @@
       if (*recordLength > 0 && record[*recordLength - 1] == '\r') {
         --*recordLength;
       }
-    } else {
-      recordLength = bytes; // final record w/o \n
+      return true;
     }
-    return true;
-  } else {
-    return false;
   }
+  return false;
 }
 
 void ExternalFileUnit::SetLeftTabLimit() {
@@ -421,7 +418,10 @@
             Frame()[recordOffsetInFrame_ + *recordLength] == '\n') {
           ++recordOffsetInFrame_;
         }
-        recordOffsetInFrame_ += *recordLength;
+        if (!resumptionRecordNumber || mayPosition()) {
+          frameOffsetInFile_ += recordOffsetInFrame_ + *recordLength;
+          recordOffsetInFrame_ = 0;
+        }
         recordLength.reset();
       }
     }
@@ -612,10 +612,17 @@
   }
   std::size_t length{0};
   do {
-    std::size_t need{recordOffsetInFrame_ + length + 1};
-    length = ReadFrame(frameOffsetInFile_, need, handler);
+    std::size_t need{length + 1};
+    length =
+        ReadFrame(frameOffsetInFile_, recordOffsetInFrame_ + need, handler) -
+        recordOffsetInFrame_;
     if (length < need) {
-      handler.SignalEnd();
+      if (length > 0) {
+        // final record w/o \n
+        recordLength = length;
+      } else {
+        handler.SignalEnd();
+      }
       break;
     }
   } while (!SetSequentialVariableFormattedRecordLength());